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Rewrite the equation with the same base.

April 24, 2026Chemistry

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Answer

x = \frac{5}{2}

6 steps

Rewrite the equation with the same base.
We know that $125 = 5^3$ . Substitute this into the equation.
$5^{x+2} = (5^3)^{x-1}$
Apply the exponent rule $(a^m)^n = a^{mn}$ .
$5^{x+2} = 5^{3(x-1)}$
Equate the exponents since the bases are the same.
$x+2 = 3(x-1)$
Distribute the 3 on the right side of the equation.
$x+2 = 3x - 3$
Gather terms with $x$ on one side and constant terms on the other side.
Subtract $x$ from both sides:
$2 = 3x - x - 3$ $2 = 2x - 3$
Add 3 to both sides:
$2 + 3 = 2x$ $5 = 2x$
Solve for $x$ .
Divide by 2:
$x = \frac{5}{2}$

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