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: 34


$x \approx -1.00$

Work Step by Step

The base in the exponential equation is $e$, so take the natural logarithm on both sides to obtain $\ln{e^{1-8x}}=\ln{7957}.$ Use the property $\ln{e^b}=b$ (where b=1-8x) on the left side to obtain $1-8x = \ln{7957}.$ Solve for $x$: $1-8x = \ln{7957} \\-8x=\ln{7957} - 1 \\x=\dfrac{\ln{7957}-1}{-8}.$ Use a calculator and round-off the answer to two decimal places to obtain $x \approx -1.00.$
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