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Expanding Logarithmic Expressions In Exercise, use the properties of logarithms to rewrite the expression as a sum, difference, or multiple of logarithms.
In (x^2(x - 1))1/2

Respuesta :

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]