Solve for R
R=3
Solve for R (complex solution)
R=\frac{2\pi n_{1}i}{3\ln(2)}+3
n_{1}\in \mathrm{Z}
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512=8^{R}
Calculate 2 to the power of 9 and get 512.
8^{R}=512
Swap sides so that all variable terms are on the left hand side.
\log(8^{R})=\log(512)
Take the logarithm of both sides of the equation.
R\log(8)=\log(512)
The logarithm of a number raised to a power is the power times the logarithm of the number.
R=\frac{\log(512)}{\log(8)}
Divide both sides by \log(8).
R=\log_{8}\left(512\right)
By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).
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