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Math Help - some simple logarithm questions

  1. #1
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    some simple logarithm questions

    i am having some problems remebering how to do these any help would be appreciated

    i) what power of 2 is equal to 37
    ii) evaluate 10^2.3 and log10 0.326
    iii) the power of 10 that is equal to 20
    iiii) the power of 2 that is equal to 50
    iiiii) log10(100)
    iiiiii) log4(256)
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by red55 View Post
    i am having some problems remebering how to do these any help would be appreciated

    i) what power of 2 is equal to 37
    The log of "a" to the base "b" is the power that "b" has to be raised to
    so it equals "a".

    So:

    b^{log_b(a)}=a

    which is virtualy the definition of a logarithm.

    So:

    2^{log_2(37)} = 37

    so here that answer is log_2(37).

    Now if you want to evaluate this on a calculator we use the change of
    base formula:

    log_2(37) = log(37)/log(2)

    where log is whatever log function you have (usually either base 10 or
    natrural).

    So:

    log_2(37) = log(37)/log(2) ~= 3.9774.

    ii) evaluate 10^2.3 and log10 0.326


    These are standard operations on your calculator

    iii) the power of 10 that is equal to 20
    iv) the power of 2 that is equal to 50
    These are both of the same form as i.

    log_10(20) = log(20)/log(10)

    log_2(50) = log(50)/log(2)

    iiiii) log10(100)
    As 10^2 = 100, no need to use a calculator here.

    iiiiii) log4(256)[/quote]

    4^2=16, 4^3=64, 4^4=256

    RonL
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