Solve for a
a = \frac{3 \log_{3} {(5)}}{2} \approx 2.197460281
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9^{a}=125
Use the rules of exponents and logarithms to solve the equation.
\log(9^{a})=\log(125)
Take the logarithm of both sides of the equation.
a\log(9)=\log(125)
The logarithm of a number raised to a power is the power times the logarithm of the number.
a=\frac{\log(125)}{\log(9)}
Divide both sides by \log(9).
a=\log_{9}\left(125\right)
By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).
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