Solve 2^m=64

$$2 ^ { m } = 64$$

Solve for m

$$m=6$$

Steps Using Definition of Logarithm

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

$$2^{m}=64$$

Take the logarithm of both sides of the equation.

$$\log(2^{m})=\log(64)$$

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

$$m\log(2)=\log(64)$$

Divide both sides by \log(2).

$$m=\frac{\log(64)}{\log(2)}$$

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

$$m=\log_{2}\left(64\right)$$

Solve for m (complex solution)

$$m=\frac{2\pi n_{1}i}{\ln(2)}+6$$

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