a = log₂18 / log₂12 = 1 + 2log₂3 / 2 + log₂3

b = log₂54 / log₂24 = 1 + 3log₂3 / 3 + log₂3

You can now just assume that log₂3 = t,

So, ab + 5(a-b) = (1 + 2t / 2 + t) + (1 + 3t) / (3 + t) + 5 [ (1 + 2t / 2 + t) - (1 + 3t / 3 + t) = 1