Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 9 - Section 9.5 - Exponential and Logarithmic Equations - Exercise Set: 34

Answer

$x \approx 3.17$

Work Step by Step

Add $4.7^x$ on both sides of the equation to obtain: $135=4.7^x$ RECALL: $\log_b{a^x} = x \cdot \log_b{a}$ Take the natural logarithm of both sides to obtain: $\ln{135}=\ln{(4.7^x)}$ Use the rule above to obtain: $\ln{135}=x \cdot \ln{(4.7)}$ Divide both sides by $\ln{(4.7)}$ to obtain: $\dfrac{\ln{135}}{\ln{4.7}}=x$ Use a scientific calculator to obtain: $3.169677962= x \\x \approx 3.17$
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