# How do you calculate  log 0.00007?

Jun 15, 2016

You can apply the scientific notation and the properties of the logarithms.

First of all

$0.00007 = 7 \cdot {10}^{-} 5$.

Then

$\log \left(0.00007\right) = \log \left(7 \cdot {10}^{-} 5\right)$

now we apply the rule $\log \left(a \cdot b\right) = \log \left(a\right) + \log \left(b\right)$

$\log \left(7 \cdot {10}^{-} 5\right) = \log \left(7\right) + \log \left({10}^{-} 5\right)$

and finally we use the property that $\log \left({a}^{b}\right) = b \cdot \log \left(a\right)$

$\log \left(7\right) + \log \left({10}^{-} 5\right) = \log \left(7\right) - 5 \log \left(10\right)$.

Now I do not know if $\log$ is with base $e$ or base $10$.
If it is base $e$ the result is $- 9.57$ otherwise it is $- 4.15$.