Question

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

Answer 1

Start by observing that:

`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 `1/2log(4)`

`log(0.06) = log(12)-2-1/2log(4)`

`log(0.06) = 1.0792-2-(0.6021)/2`

`log(0.06) = -1.2218`