Solve 5^2x=1/25

$$5 ^ { 2 x } = \frac { 1 } { 25 }$$

Solve for x

$$x=-1$$

Steps Using Definition of Logarithm

Use the rules of exponents and logarithms to solve the equation.

$$5^{2x}=\frac{1}{25}$$

Take the logarithm of both sides of the equation.

$$\log(5^{2x})=\log(\frac{1}{25})$$

The logarithm of a number raised to a power is the power times the logarithm of the number.

$$2x\log(5)=\log(\frac{1}{25})$$

Divide both sides by \log(5).

$$2x=\frac{\log(\frac{1}{25})}{\log(5)}$$

By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).

$$2x=\log_{5}\left(\frac{1}{25}\right)$$

Divide both sides by 2.

$$x=-\frac{2}{2}$$

Solve for x (complex solution)

$$x=\frac{i\pi n_{1}}{\ln(5)}-1$$

$$n_{1}\in \mathrm{Z}$$