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Math Help - Transforming Logs.

  1. #1
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    Transforming Logs.

    Please help...

    What kind of transformation is represented by
    log base b of x ----> log base (1/b) of x?


    Thank You in advance
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  2. #2
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    I would try some values for x and b and find the difference in their shapes.
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  3. #3
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    Thank You, That really helps
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  4. #4
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    Logs

    log_bx = a \ \ \ \ \ \ \ b^a = x \ \ \ \ \ \ \ \ \ \ \ \\ log_{\frac{1}{b}}x = a \ \ \ \ \ \ \ \ \ (\frac{1}{b})^a = x \ \ \ \ \ \

    Have a good day from Israel !
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  5. #5
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    Sice the question is asking for teh type of transformation, would it be wrong if i answered , The transformation is reflected on the x-axis. Meaning the y-values are negative.!

    Thank You for your help
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  6. #6
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    Quote Originally Posted by ASD2010 View Post
    Sice the question is asking for teh type of transformation, would it be wrong if i answered , The transformation is reflected on the x-axis. Meaning the y-values are negative.!

    Thank You for your help
    I would answer in the following way: \displaystyle \log_{\frac{1}{b}} (x) = - \log_b (x) therefore the transformation is reflection in the x-axis.
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  7. #7
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    More specifically, log_{\frac{1}{b}}(x)= \frac{log(x)}{log(\frac{1}{b})}= \frac{log(x)}{- log(b)} = -\frac{log(x)}{log(b)}= -log_{b}(x)
    Last edited by mr fantastic; July 28th 2010 at 06:09 AM. Reason: Fixed a typo.
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