How do you evaluate 2 log_3 12 - 2 log_3 4?

May 5, 2016

I found: $2$

Explanation:

I would use the properties of logs and write:

${\log}_{3} {\left(12\right)}^{\textcolor{red}{2}} - {\log}_{3} {\left(4\right)}^{\textcolor{red}{2}} =$

and then:

$= {\log}_{3} {\left(\frac{12}{4}\right)}^{2} = {\log}_{3} \left({3}^{2}\right) = 2$