Solve the equation.
-$( 8 ) ) ^ { x + 1 } = \left( \frac { 2 } { 4 } \right) ^ { x - 1 }$
A) $\left\{ - \frac { 1 } { 2 } \right\}$
B) $\{ - 1 \}$
C) $\left\{ \frac { 1 } { 2 } \right\}$
D) $\left\{ - \frac { 1 } { 4 } \right\}$

Question

Quizplus · Accepted Answer

First, simplify the equation. $8 = 2^3$ and $\frac{2}{4} = \frac{1}{2} = 2^{-1}$. So, the equation becomes $2^{3(x+1)} = 2^{-1(x-1)}$. Equating the exponents gives $3(x+1) = -1(x-1)$. Solving for $x$ yields $x = -\frac{1}{2}$.

Solve the Equation (8))x+1=(24)x−1( 8 ) ) ^ { x + 1 } = \left( \frac { 2 } { 4 } \right) ^ { x - 1 }(8))x+1=(42​)x−1

Solve the Equation $( 8 ) ) ^ { x + 1 } = \left( \frac { 2 } { 4 } \right) ^ { x - 1 }$