Question

What is the logarithm of 0.001 in base 10?

Answer 1

The answer is clearly `-3`. Why?

Explanation:

It is useful to remind ourselves of what a logarithm is. They can use any base. The bases that are in widespread use are logs to the base `10`, and logs to the base `e`. When we write `log_a` `b`, we are asking to what power do we raise the base `a` to get `b`. So if `log_a` `b = c`, then `a^c` = `b`. It would be worth your while to get your head round this.

So, in effect, the question asks to what power must we raise the base `10` to get `10^-3` (because, as you realize, `0.001 = 10^-3`).