Chapter 4 - Exponential and Logarithmic Functions - Section 4.6 Logarithmic and Exponential Equations - 4.6 Assess Your Understanding - Page 337: 41

$8$

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, $x-5 = 3\\ x=3+5\\ x=8$