From Log to Power

Now the unknown sits inside the log: log_2(x) = 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(x) 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(16) 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.