Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 3 - Section 3.4 - Exponential and Logarithmic Equations - Exercise Set - Page 488: 35


$x \approx 2.45$

Work Step by Step

Add 2 to both sides of the equation to obtain $e^{5x-3}-2+2=10476+2 \\e^{5x-3}=10478.$ The base in the exponential equation is $e$ so take the natural logarithm on both sides to obtain $\ln{e^{5x-3}}=\ln{10478}.$ Use the property $\ln{e^b}=b$ (where b=5x-3) on the left side to obtain $5x-3 = \ln{10478}.$ Solve for $x$: $5x-3+3 = \ln{10478}+3 \\5x=\ln{10478} +3 \\x=\dfrac{\ln{10478}+3}{5}.$ Use a calculator and round-off the answer to two decimal places to obtain $x \approx 2.45.$
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