Question

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

Answer 1

The simplified expression is:

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

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)}^(1/2)`

Applying these properties

`(1)/(2)*(\ln{x^(2) + ln((x-1)))`

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