Solve 1quad3.2^x=24

$$1 \quad 3.2 ^ { x } = 24$$

Solve for x

$$x=\log_{3.2}\left(24\right)\approx 2.732280117$$

Steps Using Definition of Logarithm

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

$$3.2^{x}=24$$

Take the logarithm of both sides of the equation.

$$\log(3.2^{x})=\log(24)$$

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

$$x\log(3.2)=\log(24)$$

Divide both sides by \log(3.2).

$$x=\frac{\log(24)}{\log(3.2)}$$

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

$$x=\log_{3.2}\left(24\right)$$

Solve for x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(3.2)}+\log_{3.2}\left(24\right)$$

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