SOLUTION: Please help me simplify: log x ( {{{ sqrt(y) }}} ) / log y ( {{{ sqrt(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:


or


Then do long division:

         2
A+2B)2A+ B
     2A+4B
       -3B

Which gives



Then we have:



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

Edwin