Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 1 - Section 1.5 - Inverse Functions and Logarithms - 1.5 Exercises - Page 67: 46

Answer

The graphs are on the figure ($f$ is blue and $g$ is red). $f$ surpasses $g$ when $x$ is approximately $3.43\cdot 10^{15}$.

Work Step by Step

The graphs are on the figure below. The logarithm is shown in red and the power function in blue. We see that in the beginning, the value of the logarithmic function is less than the value of the power function. Then $g$ surpasses $f$ at $x=3.0597\ldots$. $g$ then grows faster than $f$ and their distance increases and this looks like a trend that won't stop. But when $x$ is of the order of $10^{15}$ then we see that $f$ starts catching up and finally surpasses $g$ when $x\approx3.43\cdot10^{15}.$
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