Solve for n
n=-4
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7776\times 6^{n}=6
Use the rules of exponents and logarithms to solve the equation.
6^{n}=\frac{1}{1296}
Divide both sides by 7776.
\log(6^{n})=\log(\frac{1}{1296})
Take the logarithm of both sides of the equation.
n\log(6)=\log(\frac{1}{1296})
The logarithm of a number raised to a power is the power times the logarithm of the number.
n=\frac{\log(\frac{1}{1296})}{\log(6)}
Divide both sides by \log(6).
n=\log_{6}\left(\frac{1}{1296}\right)
By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).
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