evaluate [log2(3)] [log3(4)] [log4(5)] ... [log31(32)]

Question

evaluate [log2(3)] [log3(4)] [log4(5)] ... [log31(32)]

Answer 1

Hi Julia,

 

If log2(3) is intended ti convey log of 3 base 2 (as in log₂3), then using the change of base formula is what will help you simplify/evaluate this expression.

 

log₂3 = log 3/log 2, log_{3^{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 32 / log 2. But that can be rewritten log₂32. Looks like that has a value of 5 because 2⁵ = 32.