Solve 4^a=2

$$4 ^ { a } = 2$$

Solve for a

$$a=\frac{1}{2}=0.5$$

Steps Using Definition of Logarithm

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

$$4^{a}=2$$

Take the logarithm of both sides of the equation.

$$\log(4^{a})=\log(2)$$

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

$$a\log(4)=\log(2)$$

Divide both sides by \log(4).

$$a=\frac{\log(2)}{\log(4)}$$

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

$$a=\log_{4}\left(2\right)$$

Solve for a (complex solution)

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

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