A question on logarithms? Please help.

1. Show that log ( base 2 ) x + log ( base x ) 2-2 can be written as ( a + b )^2 / a.

Note: I think that this question is looking for the values of a and b respectively, which is supposed to be represented with a log value.
I've attempted on the method of changing the base of the logarithms. However, I do not know how to proceed.

Change the base to natural base,
log ( base 2 ) x + log ( base x ) 2-2
= lnx/ln2 + ln2/lnx - 2
= [(lnx)^2 + (ln2)^2 - 2(lnx)(ln2)]/[(lnx)(ln2)]
= [lnx - ln(2)]^2/[(lnx)(ln2)]
= (a-b)^2/(ab), where a = lnx, and b = ln2