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: 36

Answer

$x \approx 3.58$

Work Step by Step

Add 7 to both sides of the equation to obtain $e^{4x-5}-7+7=11,243+7 \\e^{4x-5}=11,250.$ The base in the exponential equation is $e$ so take the natural logarithm on both sides to obtain $\ln{e^{4x-5}}=\ln{11,250}.$ Use the property $\ln{e^b}=b$ (where b=4x-5) on the left side to obtain $4x-5 = \ln{11,250}.$ Solve for $x$: $4x-5+5 = \ln{11,250}+5 \\4x=\ln{11,250} +5 \\x=\dfrac{\ln{11,250}+5}{4}.$ Use a calculator and round-off the answer to two decimal places to obtain $x \approx 3.58.$
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