## Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

$8$
Note that $a^y = b \text{ is equivalent to } y = \log_a b$. Thus, $2^{x-5}=8\\ \longrightarrow x-5 = \log_2 8\\ x-5=\log_2{\left(2^3\right)}$ Recall: $\log_a a^r =r$ Hence, $\log_2 2^3 = 3$. Therefore, $x-5 = 3\\ x=3+5\\ x=8$