Solve 25^x=625

$$25 ^ { x } = 625$$

Solve for x

$$x=2$$

Steps Using Definition of Logarithm

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

$$25^{x}=625$$

Take the logarithm of both sides of the equation.

$$\log(25^{x})=\log(625)$$

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

$$x\log(25)=\log(625)$$

Divide both sides by \log(25).

$$x=\frac{\log(625)}{\log(25)}$$

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

$$x=\log_{25}\left(625\right)$$

Solve for x (complex solution)

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

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