Solve the equation.
-$( \sqrt { 5 } ) ^ { x + 3 } = 25 ^ { x }$
A) $\{ 1 \}$
B) $\{ 2 \}$
C) $\{ - 1 \}$
D) $\{ 3 \}$

Name: Solve the equation. -$( \sqrt { 5 } ) ^ { x + 3 } = 25 ^ { x }$ A) $\{ 1 \}$ B) $\{ 2 \}$ C) $\{ - 1 \}$ D) $\{ 3 \}$
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Question

Quizplus · Accepted Answer

Since $25 = 5^2$, we can rewrite the equation as $(\sqrt{5})^{x+3} = (5^2)^x$, which simplifies to $5^{\frac{x+3}{2}} = 5^{2x}$. Equating the exponents gives $\frac{x+3}{2} = 2x$, solving this gives $x = 1$.

Solve the Equation (5)x+3=25x( \sqrt { 5 } ) ^ { x + 3 } = 25 ^ { x }(5​)x+3=25x

Solve the Equation $( \sqrt { 5 } ) ^ { x + 3 } = 25 ^ { x }$