Given
[tex]log\sqrt[]{\frac{3x}{4x^2-9}}[/tex]
Rewritten as
[tex]\log (\frac{3x}{4x^2-9})^{\frac{1}{2}}[/tex]
Then, Apply properties of logarithms
[tex]\frac{1}{2}\log (\frac{3x}{4x^2-9})[/tex]
The logarithm of a quotient is
[tex]\frac{1}{2}\lbrack\log 3x-\log (4x^2-9)\rbrack[/tex]
And we expand each expression
[tex]\frac{1}{2}\lbrack\log 3x-\log 4x^2+\log 9\rbrack[/tex]
Answer: B
