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Rewrite the first term using the exponent rule a^m−n = (a^m)/(aⁿ).

May 25, 2026Mathematics

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x=3

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Rewrite the first term using the exponent rule $a^{m-n} = \frac{a^m}{a^n}$ .
$3^{x-1} + 3^x = 36$ $\frac{3^x}{3^1} + 3^x = 36$
Factor out $3^x$ from the terms on the left side.
$3^x \left(\frac{1}{3} + 1\right) = 36$
Simplify the expression inside the parentheses.
$3^x \left(\frac{1}{3} + \frac{3}{3}\right) = 36$ $3^x \left(\frac{4}{3}\right) = 36$
Isolate $3^x$ by multiplying both sides by the reciprocal of $\frac{4}{3}$ , which is $\frac{3}{4}$ .
$3^x = 36 \times \frac{3}{4}$ $3^x = \frac{108}{4}$ $3^x = 27$
Express 27 as a power of 3.
$3^x = 3^3$
Since the bases are the same, equate the exponents to solve for $x$ .
$x = 3$

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