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

Sep 13, 2014

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

$\log \left(100\right) = 2$
$\log \left(10\right) = 1$
$\log \left(1\right) = 0$

And:
$\log \left(\frac{1}{10}\right) = - 1$
$\log \left(.1\right) = - 1$

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: ${\log}_{2} \left(8\right) = 3$ and ${\log}_{2} \left(\frac{1}{8}\right) = - 3$
${\log}_{3} \left(9\right) = 2$ since ${3}^{2} = 9$

${\log}_{5} \left(- 5\right)$ is undefined!