Question 1154703
<pre>
{{{log((x*sqrt(y)))/log((y*sqrt(x)))=(log((x))+log((sqrt(y))))/(log((y))+log((sqrt(x))))=(log((x))+log((y^("1/2"))))/(log((y))+log((x^("1/2"))))=(log((x))+expr(1/2)log((y)))/(log((y))+expr(1/2)log((x)))=2(log((x))+expr(1/2)log((y)))/2(log((y))+expr(1/2)log((x)))=(2log((x))+log((y)))/(2log((y))+log((x)))}}}

You can quit with that answer.  But if you like you can do this:

let log(x)=A and log(y)=B, then the above becomes:

{{{(2A+B)/(2B+A)}}}
or
{{{(2A+B)/(A+2B)}}}

Then do long division:

    <u>     2</u>
A+2B)2A+ B
     <u>2A+4B</u>
       -3B

Which gives

{{{2-3B/(A+2B)}}}

Then we have:

{{{2-3log((y))/(log((x))+2log((y)))}}}

It depends on what form your teachers wants.
Both are mathematically correct.

Edwin</pre>