Chapter 4 - Exponential and Logarithmic Functions - Section 4.3 Exponential Functions - 4.3 Assess Your Understanding - Page 307: 65

$x=2$

Re-write the given equation as: $(\dfrac{1}{5})^{x}=(\dfrac{1}{5})^2$ or, $5^{-x} =5^{-2}$ Use the rule power rule: $a^p=a^q$ . We can see that the base $a=5$ is the same on both sides of the equation. So, the exponents will also be equal. This implies that $p=q$ Therefore, $5^{-x} =5^{-2} \\ -x=-2 \\ x=2$