Solve exponential equations

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Learn it If both sides are powers of the same base, the exponents must be equal. Rewrite each side with a common base, then solve the linear equation.

Example: Solve $9^{x} = 27^{x - 1}$

$9 = 3^2$ and $27 = 3^3$: $3^{2x} = 3^{3(x - 1)}$.
Exponents equal: $2x = 3x - 3$.
$x = 3$.

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