Answer
$$x=\frac{13}{3}$$
Work Step by Step
Using the rules of exponents, we find:
$$\left(2^3\right)^{x+4}=\left(2^5\right)^{3x-8} \\ 3\left(x+4\right)=5\left(3x-8\right) \\ x=\frac{13}{3}$$
Checking this solution by plugging it back in, we find that the solution is correct.
