Chapter 4 - Exponential and Logarithmic Functions - Section 4.6 Logarithmic and Exponential Equations - 4.6 Assess Your Understanding - Page 337: 42

$-2$

Note that $a^y = b \text{ is equivalent to } y = \log_a b$. Thus, $5^{-x}=25\\ \longrightarrow -x = \log_5 25\\ -x=\log_5{\left(5^2\right)}$ Recall: $\log_a a^r =r$ Hence, $\log_5 5^2 = 2$ Therefore, $-x = 2\\ x=-2$