Pre-Calculus

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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.

  • Pre-Calculus -

    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

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