Solve for b
b=\frac{1}{2}=0.5
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64^{b}=8
Use the rules of exponents and logarithms to solve the equation.
\log(64^{b})=\log(8)
Take the logarithm of both sides of the equation.
b\log(64)=\log(8)
The logarithm of a number raised to a power is the power times the logarithm of the number.
b=\frac{\log(8)}{\log(64)}
Divide both sides by \log(64).
b=\log_{64}\left(8\right)
By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).
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