Chapter 4 - Exponential and Logarithmic Functions - Section 4.3 Exponential Functions - 4.3 Assess Your Understanding - Page 307: 66

$$ x=3$$

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