Chapter 4 - Inverse, Exponential, and Logarithmic Functions - Test - Page 495: 3

$x=\frac{1}{2}$

Step 1. Convert the bases, $\frac{1}{8}=2^{-3}$ and $16=2^4$ Step 2. Rewrite the equation as $(2^{-3})^{2x-3}=(2^4)^{x+1}$ which gives $2^{-6x+9}=2^{4x+4}$ Step 3. We have $-6x+9=4x+4$, thus $10x=5$ and $x=\frac{1}{2}$