Solve 13.2^x=8

$${ 13.2 }^{ x } =8$$

Solve for x

$$x=3\log_{13.2}\left(2\right)\approx 0.805917362$$

Steps Using Definition of Logarithm

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

$$13.2^{x}=8$$

Take the logarithm of both sides of the equation.

$$\log(13.2^{x})=\log(8)$$

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

$$x\log(13.2)=\log(8)$$

Divide both sides by \log(13.2).

$$x=\frac{\log(8)}{\log(13.2)}$$

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

$$x=\log_{13.2}\left(8\right)$$

Solve for x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(13.2)}+3\log_{13.2}\left(2\right)$$

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