Solve 4=2^t

$$4 = 2 ^ { t }$$

Solve for t

$$t=2$$

Steps Using Definition of Logarithm

Swap sides so that all variable terms are on the left hand side.

$$2^{t}=4$$

Take the logarithm of both sides of the equation.

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

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

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

Divide both sides by \log(2).

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

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

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

Solve for t (complex solution)

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

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