Chapter 4 - Exponential and Logarithmic Functions - Section 4.3 Exponential Functions - 4.3 Assess Your Understanding - Page 307: 63

$ x=-4$

Re-write the given equation as: $2^{-x}=2^4$ $(Because: \ 16=2^4)$ Use the rule power rule: $a^p=a^q$ . We can see that the base $a=2$ is same on both sides of the equation. So, the exponents will also be equal. This implies that $p=q$ Therefore, $2^{-x}=2^{4} \implies x=-4$