Solve 2^a=10

$$2 ^ { a } = 10$$

Solve for a

$$a=\log_{2}\left(10\right)\approx 3.321928095$$

Steps Using Definition of Logarithm

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

$$2^{a}=10$$

Take the logarithm of both sides of the equation.

$$\log(2^{a})=\log(10)$$

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

$$a\log(2)=\log(10)$$

Divide both sides by \log(2).

$$a=\frac{\log(10)}{\log(2)}$$

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

$$a=\log_{2}\left(10\right)$$