Precalculus: Mathematics for Calculus, 7th Edition

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

Chapter 4 - Section 4.5 - Exponential and Logarithmic Functions - 4.5 Exercises - Page 368: 18

Answer

$x=\dfrac{\ln\dfrac{17}{2}}{12}\approx0.178339$

Work Step by Step

$2e^{12x}=17$ Take the $2$ to divide the right side of the equation: $e^{12x}=\dfrac{17}{2}$ Apply $\ln$ to both sides: $\ln e^{12x}=\ln\dfrac{17}{2}$ Take down the exponent $12x$ to multiply in front of the $\ln$: $12x\ln e=\ln\dfrac{17}{2}$ Since $\ln e=1$, the equation becomes: $12x=\ln\dfrac{17}{2}$ Solve for $x$: $x=\dfrac{\ln\dfrac{17}{2}}{12}\approx0.178339$
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