Question

Laws of Logarithms

Without using a calculator use the change of base rule to evaluate

1. a) log(subscript8)32(hint use base 2)
=log(subscript2 32)/log(subscript2 8) = 5/3

b) log(subscript36)1296. This one doesnt even give you a hint, so how do you know which base to use? Does it have to be a factor of 36 and 1296? Cause for the first one I could have used base four instead of 2 then.

Answer 1

log8(32) = log2(32)/log2(8) = 5/3
you are correct

log36(1296)
you don't need to change base to evaluate, since 1296 = 36^2. so log36(1296) = 2

However, now that you know that, you can use any root of 36 to change base:

log36(1296) = log6(1296)/log6(36) = 4/2 = 2