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Solve for x
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Solve for x (complex solution)
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6^{x}=\frac{1}{216}
Use the rules of exponents and logarithms to solve the equation.
\log(6^{x})=\log(\frac{1}{216})
Take the logarithm of both sides of the equation.
x\log(6)=\log(\frac{1}{216})
The logarithm of a number raised to a power is the power times the logarithm of the number.
x=\frac{\log(\frac{1}{216})}{\log(6)}
Divide both sides by \log(6).
x=\log_{6}\left(\frac{1}{216}\right)
By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).