A Graphical Approach to Algebra & Trigonometry (7th Edition)

Chapter 6

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Yes. ; A function is said to be one to one ... more

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Odd degree polynomial functions are in general not... more

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Function is one to one.  ; A function is said to ... more

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Function is one to one. ; A function is said to ... more

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Function is not one to one. ; A function is said ... more

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Function is not one to one. ; A function is said ... more

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Function is not one to one. ; A function is said ... more

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Function is not one to one. ; A function is said ... more

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Function is one to one. ; A function is said to ... more

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The function is one to one ; A function is said ... more

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Function is not one to one ; A function is said ... more

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A quadratic function with domain is not a one to ... more

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Function is one to one ; According to the ... more

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Function is one to one. ; According to the ... more

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Function is not one to one. ; According to the ... more

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Function is not one to one. ; According to the ... more

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Function is one to one. ; According to the ... more

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Function is one to one. ; According to the ... more

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Function is not one to one. ; A function is said ... more

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Not one-to-one ; Given function is . Domain of the... more

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one-to-one ; Given function is . Domain of the ... more

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one-to-one ; Given function is . Domain of the ... more

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one-to-one ; Given function is . Domain of the ... more

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one-to-one ; Given function is . Domain of the ... more

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one-to-one ; Given function is . Domain of the ... more

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not one-to-one ; Given function is .  For a ... more

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not one-to-one ; Given function is . For a ... more

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one-to-one ; When the function is one-to-one then ... more

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; For a one-to-one function no two distinct ... more

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; is the inverse of so and hence . ; is the ... more

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range ; If an element in domain of a function is... more

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; The point is on the graph of implies . Then ... more

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. ; hence, . Use this to show that and . ; more

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; If is a function with inverse function then ... more

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-3 ; If maps to then the inverse of the ... more

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does not ; For a function to have an inverse it ... more

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fourth ; Reflection of a point in the second ... more

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Consider  The above equality is obtained by using ... more

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Consider The above equality is obtained by using ... more

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Consider  The above equality is obtained by using ... more

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Consider  The above equality is obtained by using ... more

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Consider  The above equality is obtained by using ... more

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Consider  The above equality is obtained by using ... more

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is one-to-one and the inverse of ; Since for each... more

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Function is one -to- one and   the inverse ... more

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is not one-to-one. ; Since have to pre-image ... more

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is not one-to-one. ; Since have to pre-image ... more

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The function is one-to-one and  the inverse ... more

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The function is one-to-one and he inverse function... more

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 Untying your shoelaces ; Since the inverse ... more

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Releasing a car's accelerator ; Since the inverse ... more

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Exiting the room. ; Since the inverse function is ... more

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Descending the stairs. ; Since the inverse ... more

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Unwrapping the stairs. ; Since the inverse ... more

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Take off a coat. ; Since the inverse function is ... more

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the inverse function is . The domain and range  of... more

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The inverse function is and the domain and range ... more

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;   ; The given function have to be solved for ... more

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;    ; The given function have to be solved for ... more

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Function is not one-to-one. ; The value of the ... more

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Function is not on-to-one. ; The value of the ... more

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; Domain and range of is .Domain and range of ... more

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; Domain and range of is .Domain and range of ... more

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  ;  For , domain is and range is .  For , domain ... more

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; For the function  domain is   and range is . ... more

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; For  Domain is Range  is  For Domain  is  Range... more

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; Domain of is .Range of  is . Domain of is... more

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; For a one-to-one function the inverse can be ... more

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; For a one-to-one function the inverse can be ... more

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; For a one-to-one function the inverse can be ... more

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; For a one-to-one function the inverse can be ... more

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; For a one-to-one function the inverse can be ... more

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; For a one-to-one function the inverse can be ... more

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; For a one-to-one function the inverse can be ... more

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; For a one-to-one function the inverse can be ... more

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; For a one-to-one function the inverse can be ... more

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; For a one-to-one function the inverse can be ... more

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; To find the inverse, consider ; Find x in terms... more

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; Consider,  ; Solve for x in terms of y,  ; Swap... more

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2 ; To find the inverse of f(x), consider ; Solve ... more

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0 ; To find inverse of the function f, consider ; ... more

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-2 ; To find the inverse of f, consider, ; Find x ... more

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4 ;    means to find value of x, when . From the ... more

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0 ;     means to find value of x, when . From the ... more

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2 ;    means to find value of x, when . From the ... more

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0 ; By looking at the graph, when y = -2, x = 0... more

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-2 ; Look at the graph, find the value of which ... more

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-4 ; From the graph, find for which ,  ; more

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Yes ; The functions both appear to be reflective ... more

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Yes ; If and then are inverses of each other.  ... more

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No ; If is inverse of then if then should be ... more

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Yes ; The inverse of is: Swap x and y to get ... more

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Yes ; The inverse of is:Swap x and y to get the ... more

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No ; The inverse of is:Swap x and y to get ... more

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Yes ; Every value of corresponds to a unique ... more

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No ; Every value of corresponds to a unique value... more

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Take the mirror image of the graph with respect to... more

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To draw the inverse of the function take the ... more

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Take the mirror image of the graph with respect to... more

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Take the mirror image of the graph with respect to... more

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Take the reflection of points on the given line w.... more

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The points on the curve can be considered by ... more

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To build cars, dollars are required. ; .then, ... more

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sphere has radius . ;  .then, This implies, if ... more

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; Slope of a line is given as difference in ... more

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; Subsitute ; given, .then, ; Find ;  Thus, ; more

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Not a one-one function. ; Perform horizontal ... more

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The function is one-to-one and the inverse of the ... more

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; Find the inverse of substitute in place of .... more

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; Find the inverse of substitute in place of .... more

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; Substitute the numeric value of each alphabet ... more

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  ; Substitute the numerical value of alphabets in... more

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The function is one-to-one in the domains [) and... more

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The function is one-to-one in the domains [) and... more

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The function is one-to-one in the domains [) and... more

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The function is one-to-one in the domains [) and... more

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The function is one-to-one in the domains [) and... more

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The function is one-to-one in the domains [) and... more

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; Apply the given condition to solve the equation... more

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; Solving the given function, ; more

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; Solving the given equation: ; more

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; Solving the given equation: ; more

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No. ; When n is positive even, will be some ... more

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The function decreases as x goes below -3. ; Input... more

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The value of the function decreases as x increases... more

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one-to-one ; Input the function in any graph ... more

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Input the function in any graph utility platform ... more

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Input the function in any graph utility platform ... more

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Input the function in any graph utility platform ... more

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Input the function in any graph utility platform ... more

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Input both the functions in a single graph at any ... more

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Input both the functions in a single graph at any ... more

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; Given ; Applying . ; or ; Now comparing the ... more

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; write with the same base and set exponential ... more

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8.95241961947 ; Use a calculator ; more

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38.232454593 ; more

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0.375214227246 ; more

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0.0678104116011 ; more

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11.5178859516 ; more

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0.0401472058695 ; more

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13.1207790956 ; more

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0.0000962986336922 ; more

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The generated graph is of . The line touches the ... more

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The generated graph is of . The line touches the ... more

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The generated graph is of . The line touches the ... more

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The generated graph is of . The line touches the ... more

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Domain and range of exponential functions are ... more

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Domain and Range of exponential functions are ... more

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Domain and Range of exponential functions are ... more

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Domain and Range of the functions is . The ... more

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Domain and Range of the function is . The equation... more

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Domain and Range of the function is . The equation... more

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Domain: Range: Horizontal asymptote: y = ... more

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Domain: Range: Horizontal Asymptote: Decreasing ... more

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Domain: Range: Horizontal asymptote: Decreasing ... more

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Domain: Range: Horizontal asymptote: Decreasing ... more

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Let and To draw the graph for , Create a table ... more

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Let and To draw the graph , create a table for ... more

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Let and First, to create the graph for create a ... more

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Let and .First to draw the graph for y1 create a ... more

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Here, is of form where a is between 0 and 1. So... more

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Here, is of form where a is between 0 and 1. So... more

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Here, is of form where a is between 0 and 1. So... more

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Here, is of form where a is between 0 and 1. So... more

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; Make the bases same ;   ;   ;   ; more

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; Make the bases same ;   ;   ;   ; more

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; Make the bases same ;   ;   ;   ; more

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; Make the bases same ;   ;   ;   ; more

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; Using the property-Here, , and ; Using The Set... more

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; Using the property- Here, , and ; According to... more

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; Make the bases same ;   ;   ; more

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; Make the bases same ;   ;   ; more

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; Make the bases same ;   ;   ; more

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; Make the bases same ;   ;   ; more

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; Make the bases same ;   ;   ; more

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; Make the bases same ;   ;   ; more

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; Make the bases same ;   ;   ; more

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; Make the bases same ;   ;   ; more

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; Make the bases same ;   ;   ; more

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; Make the bases same ;   ;   ; more

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; First use the property of exponent and then ... more

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; First use the property of exponent and then ... more

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; First use the property of exponent and then ... more

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;Since both the graph are same that means both the... more

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The amount accumulated by 'Plan A' can be ... more

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The amount accumulated by 'Plan A' can be ... more

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The curves for interest rate compounded annually ... more

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The curve for the interest compounded annually and... more

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The number conjectured is 2,000,000 bacteria per ... more

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The function f is one to one function, therefore, ... more

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The function has an inverse. The inverse can be ... more

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; First rewrite as . Now interchange and in ... more

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; First substitute in the function and rewrite ... more

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; First substitute in the function and rewrite ... more

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; Since, the graph of is the mirror image of the... more

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; It means that 10 to the power 0 is to be raised ... more

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; It can be concluded that for all real values of... more

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Yes ; Since, the only difference between the ... more

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The value lies between the integers 1 and 2 and ... more

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The value lies between the integers -4 and -3 and... more

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; According to the definition of logarithms for ... more

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; According to the definition of logarithms for ... more

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; According to the definition of logarithms for ... more

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; According to the definition of logarithms for ... more

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; According to the definition of logarithms for ... more

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; According to the definition of logarithms for ... more

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; According to the definition of logarithms for ... more

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; According to the definition of logarithms for ... more

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; According to the definition of logarithms for ... more

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; According to the definition of logarithms for ... more

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; According to the definition of logarithms for ... more

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; According to the definition of logarithms for ... more

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; According to the definition of logarithms for ... more

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; According to the definition of logarithms for ... more

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; According to the definition of logarithms for ... more

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; According to the definition of logarithms for ... more

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Use the power rule of logarithm and evaluate .  ; ... more

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Use the power rule of logarithm and evaluate .  ; ... more

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; This equation is in the logarithm form, .First ... more

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; This equation is in the logarithm form, .First ... more

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; This equation is in the logarithm form, .First ... more

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; This equation is in the logarithm form, .First ... more

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; This equation is in the logarithm form, .First ... more

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; This equation is in the logarithm form, .First ... more

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; This equation is in the logarithm form, .First ... more

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; This equation is in the logarithm form, .First ... more

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; This equation is in the logarithm form, .First ... more

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; This equation is in the logarithm form, .First ... more

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; Using exponent property can be written as and... more

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  ; Using exponent property can be written as .... more

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1.5 ; When base value is not given, it is by ... more

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4.3 ; When base value is not given, it is by ... more

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; When base value is not given, it is by default ... more

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; When base value is not given, it is by default ... more

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; Using the property of logarithm, for all ... more

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0.5 ; Using the property of logarithm, for all ... more

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; Using the property of logarithm, for all ... more

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; Using the property of logarithm, for all ... more

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7 ; Using the property of logarithm, for all ... more

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2 ; Using the property of logarithm, for all ... more

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; In calculator, press the key and then enter ... more

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; In calculator, press the key and then enter ... more

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; In calculator, press the key and then enter ... more

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; In calculator, press the key and then enter ... more

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approximately 4.3415 ; To evaluate the value of ... more

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approximately 3.6406 ; To evaluate the value of ... more

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3.7612 approximate ; . ; more

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approximately 7.1285  ; To evaluate the value of ... more

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approximately -0.2447  ; To evaluate the value of ... more

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approximately -4.2688  ; To evaluate the value of ... more

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approximately -4.2688  ; To evaluate the value of ... more

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approximately 8.3827  ; To evaluate the value of ... more

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approximately 3.2007 ; Since of a solution with ... more

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approximately 1.7959  ; Since pH of a solution ... more

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approximately 8.4089  ; Since pH of a solution ... more

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13.4948 approximate ; Since pH of a solution with ... more

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approximately ; Since pH of a solution with ... more

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approximate ; Since pH of a solution with ... more

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approximate ; Since pH of a solution with ... more

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approximately ; Since pH of a solution with ... more

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; Apply logarithm fraction rule on and get .... more

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; Apply logarithm fraction rule on and get .Apply... more

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; Apply logarithm fraction rule on and get .Apply... more

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; Apply logarithm fraction rule on and get .Apply... more

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; Apply quotient rule on to get Apply product ... more

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; Apply quotient rule on to get Apply product ... more

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; Note that is a single logarithm with ... more

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; Note that is a single logarithm with ... more

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; Apply quotient rule and expand the single ... more

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; Apply quotient rule and expand the single ... more

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; Apply power rule to Apply quotient rule and ... more

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; Apply power rule to Apply quotient rule and ... more

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; Apply product rule and join and into a single... more

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; Apply quotient rule and join and into a ... more

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; Apply power rule to the terms and Apply ... more

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; Apply power rule to the terms and Apply ... more

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; Apply power rule to the terms and Apply ... more

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; Apply power rule to the term Apply quotient ... more

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; Apply power rule to the terms and Apply ... more

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; Apply power rule to the terms and Apply ... more

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; Apply power rule to the terms and Apply ... more

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; Apply power rule to the terms , and Group ... more

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; Apply power rule to the terms and Apply ... more

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; Using the base rule To write in exponential ... more

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; Using the base rule To write in exponential ... more

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; Using the base rule To write in exponential ... more

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;  Comparing the equation with therefore, ; ... more

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; Using the base rule To write in exponential ... more

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; Using the base rule To write in exponential ... more

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; Using the base rule To write in exponential ... more

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; Using the base rule To write in exponential ... more

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. is called an exponential function. In the given ... more

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; adding on both sides Taking (natural ... more

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; Adding on both sides Using the base rule To ... more

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; Adding on both sides  ; Taking on both sides ... more

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Using a calculator the result is Taking on both ... more

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; Using the product rule therefore, becames ; ... more

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; Using the product rule therefore, becames ; ... more

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;  using the exponent rule  Therefore  became, ; ... more

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; using the exponent rule Therefore  became, ;  ... more

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; Total number 100, similarly, ; more

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; Index Formula  for n proportions, ,, are ... more

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; To solve the given equation for , follow the ... more

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No. ; Since from the given table, the value of is... more

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To find the inverse of the given function , need ... more

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Find the values of the function at different ... more

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0.75 ; To solve the given equation, follow the ... more

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; First, convert the rate of interest into a ... more

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; To rewrite the given expression, follow the ... more

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By changing, Y1 = log (X2),  (X > 0). ; The domain... more

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For, the inverse function will be .Three points ... more

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For, the inverse function will be .Three points ... more

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For, the inverse function will be .Three points ... more

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For, the inverse function will be .Three points ... more

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For, the inverse function will be .Three points ... more

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For, the inverse function will be .Three points ... more

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Logarithmic ; is an exponential function. The ... more

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The function and are inverse functions ; The ... more

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Domain is . ; To exist then, must be true. ; ... more

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Domain is . ; To exist then, must be true.  ; ... more

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Domain is . ; To exist then, must be true. ; ... more

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Domain is . ; To exist then, must be true.  ; ... more

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Domain is . ; To exist then, must be true.  ; As... more

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Domain is . ; To exist then, must be true.  ; As... more

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Domain is . ; To exist then, must be true. ; ... more

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Domain is . ; To exist then, must be true. ; ... more

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Domain is  ; To exist then, .  ; Consider the ... more

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Domain is  . ; To exist then, must be true. ; ... more

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; To exist thenConsider the cubic equationThe ... more

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; To exist thenConsider the cubic equationThe ... more

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; To exist then It will happen in two cases when... more

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; To exist then It will happen in two cases when... more

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; To exist then Since absolute function is ... more

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; To exist then Since absolute function is ... more

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is nothing but shifting the graph of upward by 3 ... more

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is exist for all positive values of for all real ... more

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is exist for all positive values of for all real ... more

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for all real values ofSo,is exist for So   exists... more

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for all real values ofSo,is exist for So   exists... more

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for all real values of,So Therefore,   exists for... more

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Since for all real values of ,so the range of ... more

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Obtain the points on the curve by inserting random... more

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Yes, they are same. ; Observe from graph of both ... more

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; Given, function is For calculate the inverse of... more

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; Given, function is For calculate the inverse of... more

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; Given, function is For calculate the inverse of... more

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; Given, function is For calculate the inverse of... more

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-4 ; Given the function and also Suppose ... more

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6 ; Given the function and also Suppose ... more

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0.333 ; Given the function and also Suppose ... more

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1 ; Given the function and also Suppose ... more

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and   ; Given function is Now plot the two ... more

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; Given function is Now plot the two functions of... more

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; Given function is Now plot the two functions of... more

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and   ; Given function is Now plot the two ... more

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x1.164 ; 1. Given,  ; Putting on both the side ... more

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1. An exact solution is a solution in which the ... more

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; Given,  ;   ; Putting natural log or on both ... more

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; Given, ; Putting natural log or on both the ... more

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; Given,  ; Putting on both the sides we get ; more

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; Given,  ; Putting on both the sides and ... more

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; Given, solving and putting anti-log ; more

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; Simplifying the given expression and putting ... more

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; Solving given expression and putting anti-log... more

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; Solving the given expression and putting anti-... more

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; We Have ; Taking Log both sides ; more

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  ; We have ; Now in exponential form ; Putting ... more

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; We have ; In exponential Form ; Putting value ... more

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; We have ; Converting In Exponential Form ; Now ... more

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; Given equation is ; Convert the given equation ... more

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; Given equation is ; Use exponential form ; ... more

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; The equation : ; Subtract 7 from each side of ... more

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; The equation: ; Addition of  4 on both side ; ... more

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; The equation: ; Subtract 1 from both side ; ... more

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; The equation: ; Subtract 1 from both side ; ... more

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; The domain for the equation is ; Use ... more

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; The domain for the equation is , ; Use ... more

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; Addition of on both sides ; Use logarithmic ... more

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; Use logarithmic quotient rule ; Use exponential... more

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; Use logarithmic product rule ; Use exponential ... more

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; Use logarithmic product rule ; Change ... more

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; Subtract from both sides ; Apply logarithmic ... more

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; Apply logarithmic  product  rule:- ; Apply ... more

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; Apply logarithmic power rule on both side.   ; ... more

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; Substitute in the equation  ; Change ... more

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; Squaring equation on both side ; Subtract from... more

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;  Let . Substitute in  the equation ; Change ... more

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On solving the given logarithmic equation we get, ... more

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; Subtract from both sides of the equation and ... more

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; Subtract 2 from both sides of the equation and ... more

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; Subtract from both sides of the equation and ... more

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