# Assuming x and y are positive,use properties of logarithms to write the expression as a sum or difference of a logarithm or multiples of logarithms. In (x^3)/(y^3)?

Nov 21, 2016

We know that $\ln a - \ln b = \ln \left(\frac{a}{b}\right)$.

$\ln \left({x}^{3} / {y}^{3}\right) = \ln {x}^{3} - \ln {y}^{3}$

We know that $\ln {a}^{n} = n \ln a$:

$\implies 3 \ln x - 3 \ln y$

If you want it in factored form, we can have:

$\implies 3 \left(\ln x - \ln y\right)$

Hopefully this helps!