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Solve for x
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Solve for x (complex solution)
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3^{x-4}=27
Use the rules of exponents and logarithms to solve the equation.
\log(3^{x-4})=\log(27)
Take the logarithm of both sides of the equation.
\left(x-4\right)\log(3)=\log(27)
The logarithm of a number raised to a power is the power times the logarithm of the number.
x-4=\frac{\log(27)}{\log(3)}
Divide both sides by \log(3).
x-4=\log_{3}\left(27\right)
By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).
x=3-\left(-4\right)
Add 4 to both sides of the equation.