# How do you evaluate log 0.0001?

##### 1 Answer
Oct 29, 2015

$\log \left(0.0001\right) = - 4$

#### Explanation:

Recall that by the definition of logarithms:
${\log}_{a} \left(y\right) = x \iff y = {a}^{x}$
In this case:
$\log \left(0.0001\right) = x$
${10}^{x} = 0.0001 \implies$ but: $0.0001 = {10}^{-} 4$ so:
${10}^{x} = {10}^{-} 4 \implies$same bases on each side of an equation must have the same exponents, thus:
$x = - 4$