Solve for p
p=-5
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3^{p}=\frac{1}{243}
Use the rules of exponents and logarithms to solve the equation.
\log(3^{p})=\log(\frac{1}{243})
Take the logarithm of both sides of the equation.
p\log(3)=\log(\frac{1}{243})
The logarithm of a number raised to a power is the power times the logarithm of the number.
p=\frac{\log(\frac{1}{243})}{\log(3)}
Divide both sides by \log(3).
p=\log_{3}\left(\frac{1}{243}\right)
By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).
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