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