Solve 125^x=625

$$125 ^ { x } = 625$$

Solve for x

$$x = \frac{4}{3} = 1\frac{1}{3} \approx 1.333333333$$

Steps Using Definition of Logarithm

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

$$125^{x}=625$$

Take the logarithm of both sides of the equation.

$$\log(125^{x})=\log(625)$$

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

$$x\log(125)=\log(625)$$

Divide both sides by \log(125).

$$x=\frac{\log(625)}{\log(125)}$$

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

$$x=\log_{125}\left(625\right)$$

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{3\ln(5)}+\frac{4}{3}$$

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