Solve 2^3x-7=256

$$2 ^ { 3 x - 7 } = 256$$

Solve for x

$$x=5$$

Steps Using Definition of Logarithm

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

$$2^{3x-7}=256$$

Take the logarithm of both sides of the equation.

$$\log(2^{3x-7})=\log(256)$$

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

$$\left(3x-7\right)\log(2)=\log(256)$$

Divide both sides by \log(2).

$$3x-7=\frac{\log(256)}{\log(2)}$$

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

$$3x-7=\log_{2}\left(256\right)$$

Add 7 to both sides of the equation.

$$3x=8-\left(-7\right)$$

Divide both sides by 3.

$$x=\frac{15}{3}$$

Solve for x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{3\ln(2)}+5$$

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