Chapter 4 - Exponential and Logarithmic Functions - Section 4.3 Exponential Functions - 4.3 Assess Your Understanding - Page 307: 72

$x=6$

Re-write the given equation as: $(3^2)^{-x+15}=(3^3)^x$ or, $3^{-2x+30}=3^{3x}$ 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, $ -2x+30=3x \\ 30=5x \\ x =6$