Solve 4^3m=16

$$4 ^ { 3 m } = 16$$

Solve for m

$$m=\frac{2}{3}\approx 0.666666667$$

Steps Using Definition of Logarithm

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

$$4^{3m}=16$$

Take the logarithm of both sides of the equation.

$$\log(4^{3m})=\log(16)$$

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

$$3m\log(4)=\log(16)$$

Divide both sides by \log(4).

$$3m=\frac{\log(16)}{\log(4)}$$

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

$$3m=\log_{4}\left(16\right)$$

Divide both sides by 3.

$$m=\frac{2}{3}$$