# How do you evaluate log 0.001?

Nov 9, 2015

See explanation

#### Explanation:

I assume $\log$ means logarythm with base $10$. To calculate such logarythm you have to think of it as a solution to the equation:

${10}^{x} = 0.001$

So you look for a real number $x$ to which you have to raise $10$ to get $0.001$

$0.001 = \frac{1}{1000} = \frac{1}{10} ^ 3 = {10}^{- 3}$, so to get $0.001$ you have to raise $10$ to the power of $\left(- 3\right)$, so this is the solution to the equation and answer to the task:

$\log 0.001 = - 3$