Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 4 - Review - Exercises: 62

Answer

$x=\dfrac{4}{3}\ln10\approx3.07$

Work Step by Step

$e^{3x/4}=10$ Apply $\ln$ to both sides of the equation: $\ln e^{3x/4}=\ln10$ Take $\dfrac{3x}{4}$ down to multiply in front of its respective $\ln$: $\dfrac{3x}{4}\ln e=\ln10$ Since $\ln e=1$, this equation becomes: $\dfrac{3x}{4}=\ln10$ Solve for $x$: $3x=4\ln10$ $x=\dfrac{4}{3}\ln10\approx3.07$
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