Solve the equation by expressing each side as a power of the same base and then equating exponents.
-$$25 ^ { x + 8 } = 125 ^ { x - 3 }$$
A) $\{ 25 \}$
B) $\{ 11 \}$
C) $\{ 17 \}$
D) $\{ 19 \}$

Question

Quizplus · Accepted Answer

$25 = 5^2$ and $125 = 5^3$. So, the equation becomes:$$(5^2)^{x+8} = (5^3)^{x-3}$$$$5^{2x+16} = 5^{3x-9}$$Equating exponents, we get:$$2x+16 = 3x-9$$$$-x = -25$$$$x = 25$$

Solve the Equation by Expressing Each Side as a Power 25x+8=125x−325 ^ { x + 8 } = 125 ^ { x - 3 }25x+8=125x−3

Solve the Equation by Expressing Each Side as a Power $25 ^ { x + 8 } = 125 ^ { x - 3 }$