Solve 405^x=164025

$$405 ^ { x } = 164025$$

Solve for x

$$x=2$$

Steps Using Definition of Logarithm

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

$$405^{x}=164025$$

Take the logarithm of both sides of the equation.

$$\log(405^{x})=\log(164025)$$

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

$$x\log(405)=\log(164025)$$

Divide both sides by \log(405).

$$x=\frac{\log(164025)}{\log(405)}$$

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

$$x=\log_{405}\left(164025\right)$$

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(405)}+2$$

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