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Math Help - Logarithms and Logarithmic Functions

  1. #1
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    Logarithms and Logarithmic Functions

    Just found this site and looks like it can be very helpful. I'm not asking for my homework to be done, I just have a few example problems I need help with, then I can figure it out on my own. I'm in an independant study type class where I learn the material on my own, and just take the test for each chapter to pass the class. Here are some problems I can use some help with:

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    Problem 1
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    log3 y = 1/2 log3 81


    ---
    Problem 2
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    log6 (x+1) - log6 (x-1) = log6 9


    ---
    Problem 3
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    log4 n = 2 log4 8


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    Problem 4
    ---

    Use log4 7 = 1.4037 and log4 3 = 0.7925 to evaluate log 7/3


    Example: log4 = log (subscript) 4

    Thanks! I appreciate any help given!
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by toop View Post
    Just found this site and looks like it can be very helpful. I'm not asking for my homework to be done, I just have a few example problems I need help with, then I can figure it out on my own. I'm in an independant study type class where I learn the material on my own, and just take the test for each chapter to pass the class. Here are some problems I can use some help with:

    ---
    Problem 1
    ---

    log3 y = 1/2 log3 81
    i will use the following notation: log[a]b means log to the base a of b

    log[3]y = (1/2)log[3]81
    => log[3]y = log[3]81^(1/2) ...........since nlogx = log(x^n)
    => log[3]y = log[3]9
    => y = 9


    ---
    Problem 2
    ---

    log6 (x+1) - log6 (x-1) = log6 9
    log[6](x + 1) - log[6] (x - 1) = log[6]9
    => log[6]{(x + 1)/(x - 1)} = log[6]9 ............since logx - logy = log(x/y)
    => (x + 1)/(x - 1) = 9
    => x + 1 = 9x - 9
    => 8x = 10
    => x = 5/4


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    Problem 3
    ---

    log4 n = 2 log4 8
    log[4]n = 2log[4]8
    => log[4]n = log[4]8^2 ..............since nlogx = log(x^n)
    => log[4]n = log[4]64
    => n = 64


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    Problem 4
    ---

    Use log4 7 = 1.4037 and log4 3 = 0.7925 to evaluate log 7/3

    is it to evaluate log[4] (7/3)? or is it log[10]?
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  3. #3
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    Oops sorry, yes it is to log[4] (7/3)

    ...And thank you VERY much for the help on the other problems. Helped me tremendously.
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by toop View Post
    ---
    Problem 4
    ---

    Use log4 7 = 1.4037 and log4 3 = 0.7925 to evaluate log 7/3

    log[4](7/3) = log[4]7 - log[4]3 ...................since log(x/y) = logx - logy
    ................= 1.4037 - 0.7925
    ................= 0.6112
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