Solve 4^3x-3=64

$$4 ^ { 3 x - 3 } = 64$$

Solve for x

$$x=2$$

Steps Using Definition of Logarithm

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

$$4^{3x-3}=64$$

Take the logarithm of both sides of the equation.

$$\log(4^{3x-3})=\log(64)$$

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

$$\left(3x-3\right)\log(4)=\log(64)$$

Divide both sides by \log(4).

$$3x-3=\frac{\log(64)}{\log(4)}$$

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

$$3x-3=\log_{4}\left(64\right)$$

Add 3 to both sides of the equation.

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

Divide both sides by 3.

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

Solve for x (complex solution)

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

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