Find the exact solution to the equation.
-$125 \left( \frac { 1 } { 5 } \right) ^ { x / 3 } = 5$
A) $x = \frac { 2 } { 3 }$
B) $x = 7$
C) $x = 6$
D) $x = 2$

Question

Quizplus · Accepted Answer

Rewriting the equation: $125 = 5^3$ and $\left(\frac{1}{5}\right)^{x/3} = 5^{-x/3}$. Thus, $5^3 \cdot 5^{-x/3} = 5^1$. Simplifying gives $5^{3-x/3} = 5^1$, so $3 - x/3 = 1$. Solving for $x$, we get $x = 6$.

Find the Exact Solution to the Equation 125(15)x/3=5125 \left( \frac { 1 } { 5 } \right) ^ { x / 3 } = 5125(51​)x/3=5

Find the Exact Solution to the Equation $125 \left( \frac { 1 } { 5 } \right) ^ { x / 3 } = 5$