From Log to Power

Now the unknown sits inside the log: $\log_{2}\left(x\right) = 4$. A log is a power, so read it as one: 2 to the power 4 is x. That gives $x = {2}^{4}$, so $x = 16$.

Why is that allowed? Raise 2 to both sides. On the left, 2 raised to $\log_{2}\left(x\right)$ is just x, because raising to a power and taking the log undo each other. On the right, ${2}^{4}$ is 16.

Check by putting the answer back: $\log_{2}\left(16\right)$ asks which power of 2 gives 16, and that is 4. The answer always comes out positive, since a positive base to any power is positive, so it is a number the log accepts.