Solve 2.3^x=162

$$2.3 ^ { x } = 162$$

Solve for x

$$x=\log_{2.3}\left(162\right)\approx 6.108225009$$

Steps Using Definition of Logarithm

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

$$2.3^{x}=162$$

Take the logarithm of both sides of the equation.

$$\log(2.3^{x})=\log(162)$$

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

$$x\log(2.3)=\log(162)$$

Divide both sides by \log(2.3).

$$x=\frac{\log(162)}{\log(2.3)}$$

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

$$x=\log_{2.3}\left(162\right)$$

Solve for x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(2.3)}+\log_{2.3}\left(162\right)$$

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