Answer:
The simplified expression is:
[tex]\ln{x} + \frac{\ln{(x-1)}}{2}[/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{x^{2}(x-1)}^{1/2}[/tex]
Applying these properties
[tex]\frac{1}{2}*(\ln{x^{2} + \ln{(x-1)})[/tex]
[tex]\ln{x} + \frac{\ln{(x-1)}}{2}[/tex]
