Solve the equation by expressing each side as a power of the same base and then equating exponents.
-$$2 ( 3 x + 5 ) = \frac { 1 } { 16 }$$
A) $\{ - 3 \}$
B) $\left\{ \frac { 1 } { 8 } \right\}$
C) $\{ 8 \}$
D) $\{ 3 \}$

Question

Quizplus · Accepted Answer

First, express both sides of the equation as powers of 2: $2(3x + 5) = 2^{-4}$ (since $16 = 2^4$ and $\frac{1}{16} = 2^{-4}$). Simplify the left side to get $2^1(3x + 5) = 2^{-4}$, which implies $3x + 5 = 2^{-4}$. However, this step is incorrect in the process of solving the equation by expressing each side as a power of the same base. The correct approach is to solve the equation directly: $2(3x + 5) = \frac{1}{16}$, then $3x + 5 = \frac{1}{16} \times \frac{1}{2} = \frac{1}{32}$, leading to $3x = \frac{1}{32} - 5 = \frac{1 - 160}{32} = \frac{-159}{32}$, and finally $x = \frac{-159}{32 \times 3} = \frac{-159}{96}$. The mistake was in the explanation of equating powers, which is not applicable here as initially described. The correct solution involves isolating $x$ after simplifying the equation, which was not accurately followed in the explanation.

Solve the Equation by Expressing Each Side as a Power 2(3x+5)=1162 ( 3 x + 5 ) = \frac { 1 } { 16 }2(3x+5)=161​

Solve the Equation by Expressing Each Side as a Power $2 ( 3 x + 5 ) = \frac { 1 } { 16 }$