Chapter 4 - Exponential and Logarithmic Functions - Section 4.3 Exponential Functions - 4.3 Assess Your Understanding - Page 307: 71

$x=6$

Re-write the given equation as: $(2^3)^{-x+14}=(2^4)^x$ or, $2^{-3x+42}=2^{4x}$ 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, $ -3x+42=4x \\ 7x=42 \\ x =6$