Chapter 4 - Inverse, Exponential, and Logarithmic Functions - 4.5 Exponential and Logarithmic Equations - 4.5 Exercises - Page 469: 27

$x=32.9501$

The given expression can be written as: $ (1.15)^x=100 $ We need to take log of both sides and apply logarithmic property : $\log a^ b=b \log a$ . $ \log(1.15)^x=\log 100 $ and $ x \log (1.15)= \log 100 $ Now, we will evaluate the result for $x$. $x=\dfrac{\log 100}{\log 1.15 }$ Therefore, our answer is: $x=32.9501$