7
log2 3 = log 3/log 2, log3 4 = log 4/log 3 and so on. If you write out several terms you will see a pattern of numerators and denominators cancelling out. When all are cancelled it looks like what remains is log 128 / log 2= 7
Simplify the product into the form a/b for integers a and b that are relatively prime.
