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Math Help - Logarithms :(

  1. #1
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    Logarithms :(

    I need help with these just cant figure them out

    1. 3^(?) =1

    2. 3^(?) = 1/3

    3.log5 (1/25) =?

    4. logx = -0.7
    Last edited by mr fantastic; July 21st 2009 at 01:00 AM. Reason: Removed shouting
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  2. #2
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    Quote Originally Posted by icecreamfrk09 View Post
    1. 3^(?) =1
    3^x =1

    \log_3(3^x) =\log_3(1)

    x =\log_3(1)

    You can also consider a^0=1

    Quote Originally Posted by icecreamfrk09 View Post
    I
    2. 3^(?) = 1/3
    this can be the same way as Q1
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    Quote Originally Posted by icecreamfrk09 View Post
    3.log5 (1/25) =?
    \log_5(\frac{1}{25})

    = \log_5(5^{-2})

    = -2\times \log_5(5)

    = -2\times 1

    = -2
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  4. #4
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    thank you both...so both one and two are the same answer??
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  5. #5
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    What? How did you draw that conclusion? These are the most fundamental properties. You must know these or you WILL fail your exams.

    3^{1} = 3
    5^{1} = 5

    4^{0} = 1
    6^{0} = 1

    2^{-1} = 1/2
    7^{-1} = 1/7

    Look at these until you no longer feel an urge to ask the question about 1 and 2 being the same.
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    Quote Originally Posted by icecreamfrk09 View Post

    4. logx = -0.7
    This question really depends on the logs base, lets try base 10.

    log_{10}(x) = -0.7

    10^{log_{10}(x)} = 10^{-0.7}

    x = 10^{-0.7}
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  7. #7
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    k thank you tkhunny i understand now
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  8. #8
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    Quote Originally Posted by TKHunny View Post
    What? How did you draw that conclusion? These are the most fundamental properties. You must know these or you WILL fail your exams.
    To expand on this,

    3^{1} = 3 because \log_3 3 = 1
    5^{1} = 5 because \log_5 5 = 1

    4^{0} = 1 because \log_4 1 = 0
    6^{0} = 1 because \log_6 1 = 0

    2^{-1} = 1/2 because \log_2 \left(\frac{1}{2}\right) = -1
    7^{-1} = 1/7 because \log_7 \left(\frac{1}{7}\right) = -1


    01
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  9. #9
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    Quote Originally Posted by icecreamfrk09 View Post
    k thank you tkhunny i understand now
    Get used to these two things and you will do well.

    1) A Logarithm IS an Exponent.

    2) These are equivalent statements, for appropriate a, b, and c

    log_{b}(a)\;=\;c and b^{c}\;=\;a
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