Which of the following logarithm expressions are equivalent to sqrt xy in (e/x)

Answer
D) [tex]=ln(x\sqrt{xy}) - 1[/tex]
Step by step explanation
We have to use the log rules.
The given expression can be written
[tex]=ln\sqrt{xy} + ln(x) - ln(e)[/tex] [Use the quotient rule]
[tex]=ln(x\sqrt{xy}) - 1[/tex] [Use product rule : ln(x) + ln(y) = ln(xy)
and ln(e) = 1]
The answer is [tex]=ln(x\sqrt{xy}) - 1[/tex]
Thank you.