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Math Help - log base 2 basic question

  1. #1
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    log base 2 basic question

    Hello math newbie here. Sorry need to ask this basic question.

    What is the answer of


    log (base 2) (100000 + 1) - 1

    According to my info for log base 2 we divide it by log base 10 (2) for example

    5 = log base 2 (32)

    Now calculating log base 2 (32)

    log base 2 (x) = log base 10 (x) / log base 10 (2)

    So

    log base 2 (32) = log base 10 (32) / log base 10 (2)
    = 5

    Now according to the above rule my answer comes out 15.60 i.e,

    log (base 2) (100000 + 1) - 1

    = log (base 2) (100001)-1
    = 16.60 -1 = 15.60

    but in my text book this is equal to 20.

    Please tell what mistake I am doing?

    Thank You!
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  2. #2
    MHF Contributor
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    Quote Originally Posted by mrsenim View Post
    log (base 2) (100000 + 1) - 1
    According to my info for log base 2 we divide it by log base 10 (2) for example
    5 = log base 2 (32)
    Are you sure that you posted that correctly?
    Seems as silly as:
    log base 2 (31 + 1) - 1 = 4

    Or a teacher asking a poor student: whats the square root of 5 minus 1 ....
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  3. #3
    Senior Member Educated's Avatar
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    Quote Originally Posted by mrsenim View Post
    What is the answer of
    log (base 2) (100000 + 1) - 1

    = log (base 2) (100001)-1
    = 16.60 -1 = 15.60

    but in my text book this is equal to 20.

    Please tell what mistake I am doing?
    You have done nothing wrong. Your answer, 15.60 is correct, the text book answer is wrong.

    Just be careful of your rounding though. The answer comes out to be 15.60965490131... and so if you were rounding it to 2dp it would be 15.61
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