Answer:
The simplified expression is:
[tex]2\ln{x} - 3\ln{x+1}[/tex]
Step-by-step explanation:
We have those following logarithmic properties:
[tex]\ln{\frac{a}{b}} = \ln{a} - \ln{b}[/tex]
[tex]\ln{a*b} = \ln{a} + \ln{b}[/tex]
[tex]\ln{a^{n}} = n\ln{a}[/tex]
In this problem, we have that:
[tex]\ln{\frac{x^{2}}{(x+1)^{3}}}[/tex]
Applying these properties
[tex]\ln{x^{2}} - \ln{(x+1)^{3}[/tex]
[tex]2\ln{x} - 3\ln{x+1}[/tex]
