Solve 2^3x-1=32

$$2 ^ { 3 x - 1 } = 32$$

Solve for x

$$x=2$$

Steps Using Definition of Logarithm

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

$$2^{3x-1}=32$$

Take the logarithm of both sides of the equation.

$$\log(2^{3x-1})=\log(32)$$

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

$$\left(3x-1\right)\log(2)=\log(32)$$

Divide both sides by \log(2).

$$3x-1=\frac{\log(32)}{\log(2)}$$

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

$$3x-1=\log_{2}\left(32\right)$$

Add 1 to both sides of the equation.

$$3x=5-\left(-1\right)$$

Divide both sides by 3.

$$x=\frac{6}{3}$$

Solve for x (complex solution)

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

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