# How do you evaluate log 0.01 ?

Mar 22, 2016

I found $- 2$ if the log is in base $10$.

#### Explanation:

I would imagine the log base being $10$
so we write:
${\log}_{10} \left(0.01\right) = x$
we use the definition of log to write:
${10}^{x} = 0.01$
but $0.01$ can be written as: ${10}^{-} 2$ (corresponding to $\frac{1}{100}$).
so we get:
${10}^{x} = {10}^{-} 2$
to be equal we need that:
$x = - 2$
so:
${\log}_{10} \left(0.01\right) = - 2$

Mar 22, 2016

$\log 0.01 = - 2$

#### Explanation:

$\log 0.01$
$= \log \left(\frac{1}{100}\right)$
$= \log \left(\frac{1}{10} ^ 2\right)$
$= \log {10}^{-} 2$-> use property $\frac{1}{x} ^ n = {x}^{-} n$
$- 2 \log 10$->use property ${\log}_{b} {x}^{n} = n \cdot {\log}_{b} x$
$= - 2 \left(1\right)$->log 10 is 1
$= - 2$

$- 2$

#### Explanation:

$\setminus \log 0.01$

$= \setminus \log \left(\frac{1}{100}\right)$

$= \setminus \log \left({10}^{- 2}\right)$

$= - 2 \setminus \log 10$

$= - 2 \setminus \cdot 1$

$= - 2$