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Math Help - Log Problem

  1. #1
    Newbie
    Joined
    Feb 2009
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    Log Problem

    Hi,

    I am having some difficulty beginning to solve the following logarithm problem:
    Any help is very much appreciated!

    log3 (logx (log416) ) = -1 (Where 3, x, and 4 are all bases of the logs)

    I was thinking of booting the log to get:

    logx (log416) = 3^-1

    Then going:

    logx2 = 3^-1

    Then I'm stuck.

    Any suggestions?

    Thanks,

    Jim.
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  2. #2
    A riddle wrapped in an enigma
    masters's Avatar
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    Quote Originally Posted by jimstewart_NC View Post
    Hi,

    I am having some difficulty beginning to solve the following logarithm problem:
    Any help is very much appreciated!

    log3 (logx (log416) ) = -1 (Where 3, x, and 4 are all bases of the logs)

    I was thinking of booting the log to get:

    logx (log416) = 3^-1

    Then going:

    logx2 = 3^-1

    Then I'm stuck.

    Any suggestions?

    Thanks,

    Jim.
    Hi Jim,

    \log_x2=\frac{1}{3}

    x^{1/3}=2

    x^{1/3}=8^{1/3}

    x=

    How's that?
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  3. #3
    Senior Member topher0805's Avatar
    Joined
    Jan 2008
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    Vancouver
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    Quote Originally Posted by jimstewart_NC View Post
    Hi,

    I am having some difficulty beginning to solve the following logarithm problem:
    Any help is very much appreciated!

    log3 (logx (log416) ) = -1 (Where 3, x, and 4 are all bases of the logs)

    I was thinking of booting the log to get:

    logx (log416) = 3^-1

    Then going:

    logx2 = 3^-1

    Then I'm stuck.

    Any suggestions?

    Thanks,

    Jim.
    3^{-1} = \frac {1}{3}

    Therefore:

    x^{\frac {1}{3}} = 2

    Take the log (base 2) of both sides:

    \log_2 {x^\frac {1}{3}} = \log_2 2

    \frac {1}{3} \cdot \log_2 x = 1

    \log_2 x = 3

    x = 2^3

    x = 8
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  4. #4
    Newbie
    Joined
    Feb 2009
    Posts
    18

    Thank You!

    Thank you topher0805 and masters, I really appreciated your help.

    Oh, how do you get your superscript and subscript for exponents to show up?

    Thanks,

    Jim.
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  5. #5
    Senior Member topher0805's Avatar
    Joined
    Jan 2008
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    Vancouver
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    Quote Originally Posted by jimstewart_NC View Post
    Thank you topher0805 and masters, I really appreciated your help.

    Oh, how do you get your superscript and subscript for exponents to show up?

    Thanks,

    Jim.
    To do superscript: 8^x = 8^x

    Subscript: x_i = x_i

    You just need to put [tex] tags around the stuff that is math. There is a shortcut key that looks like a sigma sign.
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