quiarasimmonss9540 quiarasimmonss9540
  • 14-01-2020
  • Mathematics
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Expanding Logarithmic Expressions In Exercise, use the properties of logarithms to rewrite the expression as the sum, difference, or multiple of logarithms.
In x^2/(x + 1)^3

Respuesta :

joaobezerra joaobezerra
  • 15-01-2020

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]

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