What is the logarithm of 0.001 in base 10?

1 Answer
anor277
Jul 11, 2015

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#).

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