Solve the equation. Do not use a calculator. $$4 ^ { x + 6 } = \frac { 1 } { 16 }$$
A) $x = 2$
B) $x = 8$
C) $x = - 5 \frac { 15 } { 16 }$
D) $x = - 8$
E) $x = - 5 \frac { 1 } { 2 }$

Question

Quizplus · Accepted Answer

The equation can be solved by recognizing that $16$ is $4^2$ and thus $\frac{1}{16}$ is $4^{-2}$. Setting the exponents equal to each other gives $x + 6 = -2$, solving for $x$ gives $x = -8$.

Solve the Equation 4x+6=1164 ^ { x + 6 } = \frac { 1 } { 16 }4x+6=161​

Solve the Equation $4 ^ { x + 6 } = \frac { 1 } { 16 }$