Solve for v
v=\frac{\log_{20}\left(355\right)}{8}\approx 0.245020134
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20^{8v}=355
Use the rules of exponents and logarithms to solve the equation.
\log(20^{8v})=\log(355)
Take the logarithm of both sides of the equation.
8v\log(20)=\log(355)
The logarithm of a number raised to a power is the power times the logarithm of the number.
8v=\frac{\log(355)}{\log(20)}
Divide both sides by \log(20).
8v=\log_{20}\left(355\right)
By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).
v=\frac{\log_{20}\left(355\right)}{8}
Divide both sides by 8.
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