Find an equation of the tangent line to the graph of the function y = log10 2x, at the given point (5, 1)

Answered: Find an equation of the tangent line to…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section: Chapter Questions

Problem 9T

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Question

Find an equation of the tangent line to the graph of the function y = log₁₀ 2x, at the given point (5, 1)

Expert Solution

Step 1 Let us find the equation of the tangent line.

$G i v e n : y = \log_{10} (2 x) t h r o u g h t h e g i v e n p o i n t (5, 1) E q u a t i o n o f \tan g e n t l i n e : (y - y_{1}) = m (x - x_{1}) S l o p e : \frac{d y}{d x} = f' (x) = m$

Step 2 Solution will be at end of step(2)

$y = \log_{10} (2 x) \frac{d}{d x} (l o g_{b} x) = \frac{1}{x l n (b)} b = 10 a n d x = 2 x \frac{d y}{d x} = \frac{1}{2 x \ln (10)} . 2 \frac{d y}{d x} = \frac{1}{x \ln (10)} {\frac{d y}{d x}}_{(5, 1)} = \frac{1}{5 \ln (10)} m = \frac{1}{5 . \ln (10)} [\ln (10) = 2.302585] m = \frac{1}{11.51}$

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