Question

What is the value of the common logarithm log 10,000?

Answer 1

Logarithms in base 10 (common log) is the power of 10 that produces that number.
log(10,000) = 4 since `10^4=10000`.

Additional examples:
`log(100)=2`
`log(10)=1`
`log(1) = 0`

And:
`log(frac{1}{10})=-1`
`log(.1)=-1`

The domain of the common log as well as the logarithm in any base, is x > 0. You can not take a log of a negative number, since any positive base can NOT produce a negative number, no matter what the power!

Ex: `log_2(8)=3` and `log_2(frac{1}{8})=-3`
`log_3(9)=2` since `3^2=9`

`log_5(-5)` is undefined!