Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 4 - Inverse, Exponential, and Logarithmic Functions - 4.5 Exponential and Logarithmic Equations - 4.5 Exercises - Page 469: 30

Answer

$1$

Work Step by Step

The given expression can be written as: $5 (1.2)^{3x-2}=6 $ or, $(1.2)^{3x-2}=\dfrac{6}{5}$ We need to take log of both sides and apply logarithmic property : $\log a^ b=b \log a$ . $(3x-2) \log (1.2)=\log \dfrac{6}{5}$ Now, we will evaluate the result for $x$. $x=\dfrac{\dfrac{\log \dfrac{6}{5}}{\log 1.2 }+2}{3}$ Now, apply logarithmic property : $\log \dfrac{a}{b}=\log a - \log b$ . $x=\dfrac{\dfrac{\log 6 - \log 5}{\log 1.2}+2}{3}$ Therefore, our answer is: $x=\dfrac{1+2}{3}=1$
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