Chapter 4 - Exponential and Logarithmic Functions - Section 4.3 Exponential Functions - 4.3 Assess Your Understanding - Page 307: 68

$x=-4 $

Re-write the given equation as: $5^{x+3}=\dfrac{1}{5}$ or, $5^{x+3}=5^{-1}$ Use the rule power rule: $a^p=a^q$ . We can see that the base $a=2$ is the same on both sides of the equation. So, the exponents will also be equal. This implies that $p=q$ Therefore, $ x+3=-1 \\ x=-1-3 \\ x=-4 $