How do you solve 2 ln x - ln 3 = 2?

Jun 14, 2016

I found: $x = 4.7082$

Explanation:

We can write it as:
$\ln {x}^{2} - \ln 3 = 3$
then:
$\ln \left({x}^{2} / 3\right) = 2$
use the definition of log:
${x}^{2} / 3 = {e}^{2}$
${x}^{2} = 3 {e}^{2}$
$x = \pm \sqrt{3 {e}^{2}}$
we accept only the positive one:
$x = \sqrt{3 {e}^{2}} = 4.7082$