Solve 4^3x=48

$$4 ^ { 3 x } = 48$$

Solve for x

$$x=\frac{\log_{2}\left(3\right)+4}{6}\approx 0.930827083$$

Steps Using Definition of Logarithm

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

$$4^{3x}=48$$

Take the logarithm of both sides of the equation.

$$\log(4^{3x})=\log(48)$$

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

$$3x\log(4)=\log(48)$$

Divide both sides by \log(4).

$$3x=\frac{\log(48)}{\log(4)}$$

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

$$3x=\log_{4}\left(48\right)$$

Divide both sides by 3.

$$x=\frac{\log_{2}\left(48\right)}{2\times 3}$$