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Be careful 5^(x−2) = 3^(x-2) Find x

September 11, 2026Mathematics

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Answer

\text{2}

5 steps

Write the given equation.
$5^{x-2} = 3^{x-2}$
Divide both sides of the equation by $3^{x-2}$ .
$\frac{5^{x-2}}{3^{x-2}} = \frac{3^{x-2}}{3^{x-2}}$
Simplify both sides using the exponent rule $\frac{a^m}{b^m} = \left(\frac{a}{b}\right)^m$ .
$\left(\frac{5}{3}\right)^{x-2} = 1$
For any non-zero base $b$ , $b^0 = 1$ .
Therefore, the exponent must be equal to 0.
$x-2 = 0$
Solve for $x$ .
$x = 2$
The value of $x$ is $\boxed{\text{2}}$ .

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