Answer:
[tex]\frac{1}{2}ln(2x)-\frac{1}{2}ln(x^2-1)[/tex]
Step-by-step explanation:
In 2x/(x^2 - 1)1/2
[tex]ln(\frac{2x}{x^2-1} )^\frac{1}{2}[/tex]
Apply the property of natural log
ln x^m = m ln(x) move the exponent before ln
[tex]ln(\frac{2x}{x^2-1} )^\frac{1}{2}[/tex]
[tex]\frac{1}{2}ln(\frac{2x}{x^2-1})[/tex]
ln(m/n)= ln m - ln n
[tex]\frac{1}{2}(ln(2x)-ln(x^2-1))[/tex]
multiply 1/2 inside the terms
[tex]\frac{1}{2}ln(2x)-\frac{1}{2}ln(x^2-1)[/tex]
