Question

How do you calculate `log 0.00007`?

Answer 1

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

First of all

`0.00007 = 7*10^-5`.

Then

`log(0.00007)=log(7*10^-5)`

now we apply the rule `log(a*b)=log(a)+log(b)`

`log(7*10^-5)=log(7)+log(10^-5)`

and finally we use the property that `log(a^b)=b*log(a)`

`log(7)+log(10^-5)=log(7)-5log(10)`.

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`.