Solve 2^a=64

$$2 ^ { a } = 64$$

Solve for a

$$a=6$$

Steps Using Definition of Logarithm

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

$$2^{a}=64$$

Take the logarithm of both sides of the equation.

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

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

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

Divide both sides by \log(2).

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

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

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