# Question #e9baa

Feb 21, 2017

${\lim}_{x \to \infty} \ln \left(3 x\right) - \ln \left(2 x\right) = \ln \left(\frac{3}{2}\right)$

#### Explanation:

For any $a , b > 0$ we have that:

$\ln \left(a x\right) - \ln \left(b x\right)$

is a constant. Using the properties of logarithms:

$y \left(x\right) = \ln \left(a x\right) - \ln \left(b x\right) = \ln \left(\frac{a x}{b x}\right) = \ln \left(\frac{a}{b}\right)$.