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: 33

Answer

$x \approx 10.11$

Work Step by Step

Add $1.4^x$ on both sides of the equation to obtain: $30=^x$ RECALL: $\log_b{a^x} = x \cdot \log_b{a}$ Take the natural logarithm of both sides to obtain: $\ln{30}=\ln{(1.4^x)}$ Use the rule above to obtain: $\ln{30}=x \cdot \ln{(1.4)}$ Divide both sides by $\ln{(1.4)}$ to obtain: $\dfrac{\ln{30}}{\ln1.4}=x$ Use a scientific calculator to obtain: $10.10840424 = x \\x \approx 10.11$
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