i'm sure no one here gave you such advice for a problem of this nature. use the laws of logarithms to write the right side as a single log, then just equate what's being logged.

lnx = 2(ln3 - ln5)

=> lnx = 2(ln(3/5)) ...........since logx - logy = log(x/y)

=> lnx = ln(3/5)^2 ...........since log(x^n) = nlogx

=> lnx = ln[(3/5)^2]

=> x = (3/5)^2

=> x = 9/25

besides, even if you wanted to make lnx = y to make things look easier, you would not change ln3 and ln5 into y since they are not lnx, so going your way, you would end up with:

y = 2(ln3 - ln5) ........doing the same operations as above, you'd end up with

y = ln[(3/5)^2]

but y = lnx

=> lnx = ln[(3/5)^2]

=> x = 9/25