Question

Expanding logarithmic Expression In Exercise,Use the properties of logarithms to rewrite the expression as a sum,difference,or multipal of logarithms.See example 3.

In 2x/(x^2 - 1)1/2

Answer 1

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

Explanation:

In 2x/(x^2 - 1)1/2

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

Apply the property of natural log

ln x^m = m ln(x) move the exponent before ln

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

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

ln(m/n)= ln m - ln n

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

multiply 1/2 inside the terms

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