   Chapter 4.5, Problem 52E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Finding an Equation of a Tangent Line InExercises 45-52, find an equation of the tangent line to the graph of the function at the given point. See Example 5. g ( x ) = log 8 4 x ;    ( 2 , 1 )

To determine

To calculate: The equation of the tangent to the graph of the function g(x)=log84x at the point (2,1).

Explanation

Given information:

The provided function is g(x)=log84x and the point is (2,1).

Formula used:

Product rule of derivative of differentiable functions, f(x) and g(x) is:

ddx[f(x)g(x)]=f(x)g(x)+f(x)g(x).

The derivative of function f(x)=un using the chain rule is:

f(x)=ddx(un)=nun1dudx

Where, u is the function of x.

Equation of line is y=mx+b where m is the slope and b=y1mx1 when line passes through (x1,y1).

Calculation:

Consider the function,

g(x)=log84x

Apply the properties of change-of-base rule to the function g(x)=log84x,

g(x)=log84x=ln4xln8

Apply logarithmic rule of derivative to the function g(x)=log84x,

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