5 log 3 = a 2 log 5 = b 15 log 40?

5 log 3 = a
2 log 5 = b
15 log 40 = log 40/log 15
=2 log (8×5)/2 log (5×3)
=(2 log 8+2 log 5)/(2 log 5+2 log 3)
=(2 log 8+2 log 5)/(2 log 5+(2 log 5×5 log3))
=(3+b)/(a+ab)
=(3+b)/(a(1+b))