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Math Help - Logarithmic equation

  1. #1
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    Logarithmic equation

    For what value of is the following equation true?

     (log x )^3 = 4 log x


    So I need 3 X values I suppose and I need them rounded to 4 decimal places. So if I can figure out how to work this I should be fine. But I don't even know where to start the problem. Help would be greatly appreciated.
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by n8thatsme View Post
    For what value of is the following equation true?

     (log x )^3 = 4 log x


    So I need 3 X values I suppose and I need them rounded to 4 decimal places. So if I can figure out how to work this I should be fine. But I don't even know where to start the problem. Help would be greatly appreciated.
    lets see if this gives you any ideas. let \log x = y, you have

    y^3 = 4y

    can you solve for y?
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  3. #3
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    I guess y would be equal to the cube root of 4y? I don't understand why I have 2 y's, should there just be one y and one x?
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    Quote Originally Posted by n8thatsme View Post
    I guess y would be equal to the cube root of 4y? I don't understand why I have 2 y's, should there just be one y and one x?
    that is not solving for y. to solve for y, you have to get y on one side of the equation by itself

    y^3 = 4y

    \Rightarrow y^3 - 4y = 0

    \Rightarrow y(y^2 - 4) = 0

    now what?
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    I got y = 0, -2, 2 but those aren't the correct answers.
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by n8thatsme View Post
    I got y = 0, -2, 2 but those aren't the correct answers.
    of course not, you were asked to solve for x, y = \log x, and thus it is not your solution, it is the log of your solutions

    you must take the antilog of those values (if they exist)
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  7. #7
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    We haven't learned antilogs yet. So I would plug in my y values into the equation so for example: y=0 it would be: (0)^3=4(0)?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by n8thatsme View Post
    We haven't learned antilogs yet. So I would plug in my y values into the equation so for example: y=0 it would be: (0)^3=4(0)?
    no, what good would that do. we already know 0 = 0

    i assure you that you have learned antilogs. these are just returning the logs to their exponential counterparts. logs are defined to make this easy transition

    \log_a b = c \Longleftrightarrow a^c = b
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