# Given log(4)=0.6021, log(9)=0.9542, and log(12)=1.0792, how do you find log(0.06)?

Oct 11, 2017

Start by observing that:

$\frac{12}{0.06} = 200$

Then ask yourself the question; "How do we divide by 200 using base 10 logarithms?"

In base 10, we divide by 100 by subtracting 2.

And divide by 2 by subtracting $\frac{1}{2} \log \left(4\right)$

$\log \left(0.06\right) = \log \left(12\right) - 2 - \frac{1}{2} \log \left(4\right)$

$\log \left(0.06\right) = 1.0792 - 2 - \frac{0.6021}{2}$

$\log \left(0.06\right) = - 1.2218$