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: 38

Answer

$x \approx 6.06$

Work Step by Step

The base in the exponential equation is $5$, so take the natural logarithm on both sides to obtain $\ln{5^{x-3}}=\ln{137}.$ Use the power rule $\ln{a^x}=x\ln{a}$ to bring down the exponent: $(x-3)\ln{5} = \ln{137}.$ Divide both sides by $\ln{5}$ to obtain $x-3 = \dfrac{\ln{137}}{\ln{5}}.$ Add $3$ to both sides to obtain $x = \dfrac{\ln{137}}{\ln{5}}+3.$ Use a calculator and round-off the answer to two decimal places to obtain $x \approx 6.06.$
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