# How do you evaluate log 0.001 + log 100?

Jul 7, 2016

$\log 0.001 + \log 100 = - 1$

#### Explanation:

The common logarithm $\log \left(x\right)$ and exponentiation ${10}^{x}$ are essentially inverse functions of one another.

So we find:

$\log 0.001 + \log 100 = \log \left({10}^{- 3}\right) + \log \left({10}^{2}\right) = - 3 + 2 = - 1$

Note also that in general we have:

$\log \left(a\right) + \log \left(b\right) = \log \left(a b\right)$

So:

$\log 0.001 + \log 100 = \log \left(0.001 \cdot 100\right) = \log \left(0.1\right) = \log \left({10}^{- 1}\right) = - 1$