Solve the equation by expressing each side as a power of the same base and then equating exponents.
-$$4 ( 3 x + 5 ) = \frac { 1 } { 256 }$$
A) $\{ - 3 \}$
B) $\left\{ \frac { 1 } { 64 } \right\}$
C) $\{ 128 \}$
D) $\{ 3 \}$

Question

Quizplus · Accepted Answer

First, express both sides of the equation as powers of 2: $4 = 2^2$ and $256 = 2^8$. Thus, the equation becomes $2^2(3x + 5) = 2^{-8}$. Simplifying, we get $2^{2(3x + 5)} = 2^{-8}$, leading to $2(3x + 5) = -8$. Solving for $x$, we find $x = -3$.

Solve the Equation by Expressing Each Side as a Power 4(3x+5)=12564 ( 3 x + 5 ) = \frac { 1 } { 256 }4(3x+5)=2561​

Solve the Equation by Expressing Each Side as a Power $4 ( 3 x + 5 ) = \frac { 1 } { 256 }$