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Math Help - Prove this logarithmic eaquation

  1. #1
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    Prove this logarithmic eaquation

    Hi,
    Can anybody prove this quation please?
    thanks in advance
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  2. #2
    Senior Member BAdhi's Avatar
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    use log_a(b)=\frac{1}{log_b(a)}

    Spoiler:

    \log_a(N)\log_b(N)+\log_b(N)\log_c(N)+\log_c(N)\lo  g_a(N)=\log_a(N)\log_b(N)\log_c(N)[\frac{1}{\log_a(N)}+\frac{1}{\log_b(N)}+\frac{1}{\  log_c(N)}]

    =\log_a(N)\log_b(N)\log_c(N)[\log_N(a)+\log_N(b)+\log_N(c)]

    =\log_a(N)\log_b(N)\log_c(N)[\log_N(abc)]=\log_a(N)\log_b(N)\log_c(N)\frac{1}{\log_{abc}(N)  }
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  3. #3
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    Here is another way.
    \log_a(N)=\dfrac{\ln(N)}{\ln(a)} use that to change all on the left hand side.
    You can get LHS to equal \dfrac{[\ln(N)]^2[\ln(abc)]}{ \ln(a) \ln(b) \ln(c)}.

    Work on the RHS you can reduce it. Equality will follow.
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