Question

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

Answer 1

The simplified expression is:

`2ln(x) - 3ln(x+1)`

Explanation:

We have those following logarithmic properties:

`\ln{(a)/(b)} = ln(a) - ln(b)`

`ln(a*b) = ln(a) + ln(b)`

`\ln{a^(n)} = nln(a)`

In this problem, we have that:

`\ln{(x^(2))/((x+1)^(3))}`

Applying these properties

`\ln{x^(2)} - \ln{(x+1)^(3)`

`2ln(x) - 3ln(x+1)`