5.2 Logs base 10

$$\fbox{$10^{??} = 1000.$ }$$

In English: to what power do I have to raise 10 to get 1000?

The logarithm of 1000 base 10 is 3.

10^?? = 1,000,000.

10^?? = 1,000,000,000.

So logarithms to base 10 can be used to summarize variables into magnitude ``bins'', for example the Executive Compensation dataset.

What the log curve looks like: looks like.

Describe this in English:

It's an increasing relationship, but it grows at an ever decreasing rate.