Solve 2^3x+3=64

$$2 ^ { 3 x + 3 } = 64$$

Solve for x

$$x=1$$

Steps Using Definition of Logarithm

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

$$2^{3x+3}=64$$

Take the logarithm of both sides of the equation.

$$\log(2^{3x+3})=\log(64)$$

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

$$\left(3x+3\right)\log(2)=\log(64)$$

Divide both sides by \log(2).

$$3x+3=\frac{\log(64)}{\log(2)}$$

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

$$3x+3=\log_{2}\left(64\right)$$

Subtract 3 from both sides of the equation.

$$3x=6-3$$

Divide both sides by 3.

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

Solve for x (complex solution)

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

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