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Math Help - Logarithms

  1. #1
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    Logarithms

    Thanks for your help in advance..

    If  a = \log_{10} \frac{10}{9} , b = \log_{10} \frac{25}{24} and <br />
c = \log_{10} \frac{81}{80}

    prove that \log_{10} 2 = 7a-2b+3c
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  2. #2
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    Quote Originally Posted by ecogreen View Post
    Thanks for your help in advance..

    If  a = \log_{10} \frac{10}{9} , b = \log_{10} \frac{25}{24} and <br />
c = \log_{10} \frac{81}{80}

    prove that \log_{10} 2 = 7a-2b+3c

    7a-2b+3c=7\log\frac{10}{9}-2\log\frac{25}{24}+3\log\frac{81}{80} =7(\log 2+\log 5-2\log 3)-2(2\log 5-3\log 2-\log 3)+3(4\log 3-4\log 2 -\log 5) , and now open up parenthese and you're done.

    Logarithms' properties used: \log\frac{A}{B}=\log A-\log B\,,\,\log(AB)=\log A+\log B\,,\,\log(A^n)=n\log A

    Tonio
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