Solve for a
a=6
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\frac{1}{81}\times 3^{a}=9
Use the rules of exponents and logarithms to solve the equation.
3^{a}=729
Multiply both sides by 81.
\log(3^{a})=\log(729)
Take the logarithm of both sides of the equation.
a\log(3)=\log(729)
The logarithm of a number raised to a power is the power times the logarithm of the number.
a=\frac{\log(729)}{\log(3)}
Divide both sides by \log(3).
a=\log_{3}\left(729\right)
By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).
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