Solve for k
k=9
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2^{k}=512
Use the rules of exponents and logarithms to solve the equation.
\log(2^{k})=\log(512)
Take the logarithm of both sides of the equation.
k\log(2)=\log(512)
The logarithm of a number raised to a power is the power times the logarithm of the number.
k=\frac{\log(512)}{\log(2)}
Divide both sides by \log(2).
k=\log_{2}\left(512\right)
By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).
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