Solve for n
n=-\log_{110}\left(3855\right)\approx -1.75665584
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110^{n}=\frac{1}{3855}
Use the rules of exponents and logarithms to solve the equation.
\log(110^{n})=\log(\frac{1}{3855})
Take the logarithm of both sides of the equation.
n\log(110)=\log(\frac{1}{3855})
The logarithm of a number raised to a power is the power times the logarithm of the number.
n=\frac{\log(\frac{1}{3855})}{\log(110)}
Divide both sides by \log(110).
n=\log_{110}\left(\frac{1}{3855}\right)
By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).
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