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Math Help - Logarithm question

  1. #1
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    Logarithm question

    If x,y,z>0, xy\neq1, yz\neq1, zx\neq1 and xyz\neq1, then \frac{1}{\log_{xy}(xyz)} +\frac{1}{\log_{yz}(xyz)}+\frac{1}{\log_{zx}(xyz)}  =

    a)1

    b)2

    c)3

    d)4

    I am new to logarithm. I know only the basics. Can anyone tell me from where I can learn logarithm in detail. Thanks in advance.

    This question is from the sample paper of my entrance exam I need to learn algorithm to this level so that I can get clear.
    I hope someone can help . Thanks once more time in advance.
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  2. #2
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    Quote Originally Posted by siddscool19 View Post
    If x,y,z>0, xy\neq1, yz\neq1, zx\neq1 and xyz\neq1, then \frac{1}{\log_{xy}(xyz)} +\frac{1}{\log_{yz}(xyz)}+\frac{1}{\log_{zx}(xyz)}  =

    a)1

    b)2

    c)3

    d)4

    I am new to logarithm. I know only the basics. Can anyone tell me from where I can learn logarithm in detail. Thanks in advance.

    This question is from the sample paper of my entrance exam I need to learn algorithm to this level so that I can get clear.
    I hope someone can help . Thanks once more time in advance.
    Hint: b) is the answer.
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  3. #3
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    Lexington, MA (USA)
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    Hello, siddscool19!

    If x,y,z\,>\,0,\;xy\neq1,\:yz\neq1,\:xz\neq1,\:xyz\ne  q1,

    then: . \frac{1}{\log_{xy}(xyz)} + \frac{1}{\log_{yz}(xyz)}+\frac{1}{\log_{zx}(xyz)} equals:

    . . (a)\;1 \qquad (b)\;2 \qquad (c)\;3\qquad (d)\;4
    We're expected to know this identity: . \log_a(b) \:=\:\frac{1}{\log_b(a)}


    Then: . \frac{1}{\log_{xy}(xyz)} \;+\; \frac{1}{\log_{yz}(xyz)} \;+\; \frac{1}{\log_{zx}(xyz)} \;\;=\;\;\log_{xyz}(xy) \;+\; \log_{xyz}(yz) \;+\; \log_{xyz}(zx)


    . . . = \;\;\log_{xyz}(xy\cdot yz \cdot zx) \;\;=\; \;\log_{xyz}(x^2y^2z^2) \;\;=\;\;\log_{xyz}(xyz)^2


    . . . = \;\;2\cdot\underbrace{\log_{xyz}(xyz) }_{\text{This is 1}}\;\;= \;\;2 \quad\hdots\;\;{\color{blue}\text{answer (b)}}

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  4. #4
    MHF Contributor
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    Quote Originally Posted by siddscool19 View Post
    I am new to logarithm. I know only the basics. Can anyone tell me from where I can learn logarithm in detail.
    To learn about logs, try the following:

    . . . . .Google results for "logarithms introduction"
    . . . . .Google results for "log rules"
    . . . . .Google results for "graphing logarithmic functions"
    . . . . .Google results for "solving logarithmic equations"
    . . . . .Google results for "logarithmic word problems"

    Have fun!
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