Solve the equation by expressing each side as a power of the same base and then equating exponents.
-$$8 ( x - 10 ) / 6 = \sqrt { 8 }$$
A) $\{ 13 \}$
B) $\{ 22 \}$
C) $\{ 16 \}$
D) $\{ 12 \}$

Question

Quizplus · Accepted Answer

First, express both sides of the equation as powers of 2: $8 = 2^3$ and $\sqrt{8} = 2^{\frac{3}{2}}$. Thus, the equation becomes $2^3 \cdot \frac{x - 10}{6} = 2^{\frac{3}{2}}$. Equating the exponents gives $\frac{x - 10}{6} = \frac{3}{2}$. Solving for $x$ yields $x = 13$.

Solve the Equation by Expressing Each Side as a Power 8(x−10)/6=88 ( x - 10 ) / 6 = \sqrt { 8 }8(x−10)/6=8​

Solve the Equation by Expressing Each Side as a Power $8 ( x - 10 ) / 6 = \sqrt { 8 }$