Solve 2+2=3^x

$$2 + 2 = 3 ^ { x }$$

Solve for x

$$x=2\log_{3}\left(2\right)\approx 1.261859507$$

Steps Using Definition of Logarithm

Add 2 and 2 to get 4.

$$4=3^{x}$$

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

$$3^{x}=4$$

Take the logarithm of both sides of the equation.

$$\log(3^{x})=\log(4)$$

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

$$x\log(3)=\log(4)$$

Divide both sides by \log(3).

$$x=\frac{\log(4)}{\log(3)}$$

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

$$x=\log_{3}\left(4\right)$$

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(3)}+2\log_{3}\left(2\right)$$

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