What are logs in math? Do you use them to develop a foundation and build like beavers do? No, you don’t. Instead, in math, logs are the “opposite” of exponentials, just as subtraction is the opposite of addition. If I asked you what number (x) to the third power equals 8 (x^{3} = 8), then you would take the cube root of both sides and tell me the cube root of 8 equals 2.

Now consider this: if I asked you 2 raised to what power (x) gets you 8, how would you solve it? Well, we know that x=3 because 2^{3} = 8, as we saw from the previous problem. But what steps would you take to solve this problem, or any others like it? As I mentioned before, logs are the “opposite”, or the inverse, of exponentials. Thus, one operation can undo the other. Let’s take a look at the relationship between them.