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Math Help - Log Functions...Find a

  1. #1
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    Log Functions...Find a

    Find a so that the graph of f(x) = log_a (x) contains the point (1/2, -4).

    NOTE: log_a (x) = "log sub a x"
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  2. #2
    Senior Member nikhil's Avatar
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    Quote Originally Posted by magentarita View Post
    Find a so that the graph of f(x) = log_a (x) contains the point (1/2, -4).

    NOTE: log_a (x) = "log sub a x"
    (1/2,-4) will satisfy the equation
    -4=log_a (1/2)
    a^-4=1/2
    a^4=2
    therfor
    a=+2^(1/4) as a can not be <0
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  3. #3
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    Quote Originally Posted by magentarita View Post
    Find a so that the graph of f(x) = log_a (x) contains the point (1/2, -4).

    NOTE: log_a (x) = "log sub a x"
    Let y=\log _a x

    (x, y) \implies \left(\frac12, -4\right) \implies x=\frac12, y=-4

    \therefore -4 = \log _a \left(\frac12\right)

    The general rule to simplify this is: \log _a n = x \implies a^x = n

    \therefore -4 = \log _a \left(\frac12\right) \implies a^{-4} = \frac12

    \therefore a = \sqrt[-4] {\frac12} = \left(\frac12\right)^{-\frac14}

    \therefore a = (2)^{\frac14} = \sqrt[4]2 \approx 1.19\text{ to 3 s.f}
    Last edited by Simplicity; August 1st 2008 at 03:33 AM. Reason: Latex correction and to avoid confusion
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    Great Work!

    I thank both of you, especially Air for his use of LATEX.
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  5. #5
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    Quote Originally Posted by magentarita View Post
    I thank both of you, especially Air for his use of LATEX.
    You fell for the old gender bias trap ...... I believe that s/he is XX not XY ....
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