Solve 2^t2=4

$$2 ^ { t 2 } = 4$$

Solve for t_2

$$t_{2}=2$$

Steps Using Definition of Logarithm

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

$$2^{t_{2}}=4$$

Take the logarithm of both sides of the equation.

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

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

$$t_{2}\log(2)=\log(4)$$

Divide both sides by \log(2).

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

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

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