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Thread: monotonous decreasing function

  1. #1
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    monotonous decreasing function

    May I call "log1/3n as a monotonous decreasing function?(1/3 is the base)
    According to the book it is not. According to me it is.
    it becomes -( logn/log3) and it decreases as n changes.

    I can't write some symbols. an+1-an<0
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  2. #2
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    Re: monotonous decreasing function

    Yes, log_{1/3}(x)= -\frac{log(x)}{3} is a monotone, decreasing function.

    More generally, log_a(x) is monotone increasing if a> 1, monotone decreasing for 0< a< 1.
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  3. #3
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    Re: monotonous decreasing function

    I believe you mean "monotonic"

    In English "monotonous" means boring.

    $\ln\left(\dfrac {1}{3n}\right)$ is monotonic for $n\geq 1$

    I can't imagine why your book says it is not.
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    Re: monotonous decreasing function

    Many Thanks.
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    Re: monotonous decreasing function

    Quote Originally Posted by romsek View Post


    $\ln\left(\dfrac {1}{3n}\right)$ is monotonic for $n\geq 1$

    I can't imagine why your book says it is not.
    It's not that expression. The OP stated that 1/3 is the base, not part of the argument.
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  6. #6
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    Re: monotonous decreasing function

    Quote Originally Posted by kastamonu View Post
    May I call "log1/3n as a monotonous decreasing function?(1/3 is the base)
    According to the book it is not. According to me it is.
    it becomes -( logn/log3) and it decreases as n changes.

    I can't write some symbols. an+1-an<0
    Maybe your book just means the function is not boring!
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