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: 28

Answer

$x=6.5788$

Work Step by Step

The given expression can be written as: $ (0.9)^x=0.5 $ We need to take log of both sides and apply logarithmic property : $\log a^ b=b \log a$ . $ \log(0.9)^x=\log 0.5 $ and $ x \log (0.9)= \log 0.5 $ Now, we will evaluate the result for $x$. $x=\dfrac{\log 0.5}{\log 0.9 }$ Therefore, our answer is: $x=6.5788$
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