Solve 5^5n=25

$$5 ^ { 5 n } = 25$$

Solve for n

$$n=\frac{2}{5}=0.4$$

Steps Using Definition of Logarithm

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

$$5^{5n}=25$$

Take the logarithm of both sides of the equation.

$$\log(5^{5n})=\log(25)$$

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

$$5n\log(5)=\log(25)$$

Divide both sides by \log(5).

$$5n=\frac{\log(25)}{\log(5)}$$

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

$$5n=\log_{5}\left(25\right)$$

Divide both sides by 5.

$$n=\frac{2}{5}$$

Solve for n (complex solution)

$$n=\frac{i\times 2\pi n_{1}}{5\ln(5)}+\frac{2}{5}$$

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