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Solve for x
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Solve for x (complex solution)
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0.25^{x-3}=32
Use the rules of exponents and logarithms to solve the equation.
\log(0.25^{x-3})=\log(32)
Take the logarithm of both sides of the equation.
\left(x-3\right)\log(0.25)=\log(32)
The logarithm of a number raised to a power is the power times the logarithm of the number.
x-3=\frac{\log(32)}{\log(0.25)}
Divide both sides by \log(0.25).
x-3=\log_{0.25}\left(32\right)
By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).
x=-\frac{5}{2}-\left(-3\right)
Add 3 to both sides of the equation.