Chapter 4 - Inverse, Exponential, and Logarithmic Functions - 4.5 Exponential and Logarithmic Equations - 4.5 Exercises - Page 469: 29

$7.044$

The given expression can be written as: $3 (2)^{x-2}=99 $ or, $2^{x-2}=33$ We need to take log of both sides and apply logarithmic property : $\log a^ b=b \log a$ . $ (x-2) \log 2= \log 33$ Now, we will evaluate the result for $x$. $x=\dfrac{\log 33}{\log 2 }+2$ Therefore, our answer is: $x \approx 7.044$