Solve the equation.
-$$( \sqrt { 5 } ) ^ { x + 5 } = 25 ^ { x }$$
A) $\left\{ \frac { 5 } { 3 } \right\}$
B) $\{ 1 \}$
C) $\left\{ \frac { 10 } { 3 } \right\}$
D) $\{ 5 \}$

Question

Quizplus · Accepted Answer

First, express 25 as $5^2$. The equation becomes $(\sqrt{5})^{x+5} = (5^2)^x$. Simplify to get $5^{\frac{x+5}{2}} = 5^{2x}$. Equating exponents gives $\frac{x+5}{2} = 2x$, solving this gives $x = \frac{5}{3}$.

Solve the Equation (5)x+5=25x( \sqrt { 5 } ) ^ { x + 5 } = 25 ^ { x }(5​)x+5=25x

Solve the Equation $( \sqrt { 5 } ) ^ { x + 5 } = 25 ^ { x }$