Solve 4^m*4^2=4^12

$$4 ^ { m } \times 4 ^ { 2 } = 4 ^ { 12 }$$

Solve for m

$$m=10$$

Steps Using Definition of Logarithm

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

$$16\times 4^{m}=16777216$$

Divide both sides by 16.

$$4^{m}=1048576$$

Take the logarithm of both sides of the equation.

$$\log(4^{m})=\log(1048576)$$

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

$$m\log(4)=\log(1048576)$$

Divide both sides by \log(4).

$$m=\frac{\log(1048576)}{\log(4)}$$

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

$$m=\log_{4}\left(1048576\right)$$