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Solve for x
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Solve for x (complex solution)
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5^{2x+1}=\frac{1}{25}
Use the rules of exponents and logarithms to solve the equation.
\log(5^{2x+1})=\log(\frac{1}{25})
Take the logarithm of both sides of the equation.
\left(2x+1\right)\log(5)=\log(\frac{1}{25})
The logarithm of a number raised to a power is the power times the logarithm of the number.
2x+1=\frac{\log(\frac{1}{25})}{\log(5)}
Divide both sides by \log(5).
2x+1=\log_{5}\left(\frac{1}{25}\right)
By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).
2x=-2-1
Subtract 1 from both sides of the equation.
x=-\frac{3}{2}
Divide both sides by 2.