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Solve for x (complex solution)
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5^{3x-1}=\frac{1}{5}
Use the rules of exponents and logarithms to solve the equation.
\log(5^{3x-1})=\log(\frac{1}{5})
Take the logarithm of both sides of the equation.
\left(3x-1\right)\log(5)=\log(\frac{1}{5})
The logarithm of a number raised to a power is the power times the logarithm of the number.
3x-1=\frac{\log(\frac{1}{5})}{\log(5)}
Divide both sides by \log(5).
3x-1=\log_{5}\left(\frac{1}{5}\right)
By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).
3x=-1-\left(-1\right)
Add 1 to both sides of the equation.
x=\frac{0}{3}
Divide both sides by 3.