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Math Help - Logarithm numbers

  1. #1
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    Logarithm numbers

    Thanks a lot for all your help in advance.


    If  \log_{10} (n+1) - \log_{10} n < \log_{10} 1.01 find the smallest positive integral value for n.
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    Quote Originally Posted by ecogreen View Post
    Thanks a lot for all your help in advance.


    If  \log_{10} (n+1) - \log_{10} n < \log_{10} 1.01 find the smallest positive integral value for n.
    \log_{10}{(n + 1)} - \log_{10}{n} < \log_{10}{1.01}

    \log_{10}{\frac{n + 1}{n}} < \log_{10}{1.01}

    \frac{n + 1}{n} < 1.01

    1 + \frac{1}{n} < 1.01

    \frac{1}{n} < 0.01

    \frac{1}{n} < \frac{1}{100}

    n > 100.


    Therefore the smallest possible integer value for n is 101.
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