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Dee W
Lv 7
Dee W asked in Science & MathematicsMathematics · 1 decade ago

log[x]y = -log[1/x] y?

Please help, I don't remember exactly how to do this.

3 Answers

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  • DWRead
    Lv 7
    1 decade ago
    Favorite Answer

    Use the Change of Base Rule for logarithms

    http://www.flickr.com/photos/dwread/4128001993/

  • andreydy
    1 decade ago

    -log(1/x) = -(log1 - logx) = -(0 - logx) = logx

    so,

    log(x)y not equals -log(x)y

  • ?
    Lv 7
    1 decade ago

    -log_(1/x) (y)

    = log_(1/x) (y)^(-1)

    = log_(1/x) (1/y)

    = [log_(x) (1/y)] / [log_(x) (1/x)]

    = [log_(x) (1/y)] / [log_(x) (x)^(-1)]

    = [log_(x) (1/y)] / [-log_(x) (x)]

    = log_(x) (1/y) / (-1)

    = -log_(x) (1/y)

    = log_(x) (1/y)^(-1)

    = log_(x) (y)

    Properties of log:

    a log (b) = log (b)^a

    log_(a) (b) = log_(c) (b) / log_(c) (a)

    log_(a) (a) = 1

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