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Thread: solve for x: with log bases

  1. October 23rd 2006, 07:19 PM #1
    robinpatrick
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    solve for x: with log bases

    solve for x: log7(x+8) - log7(x-1) = log710
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  2. October 23rd 2006, 07:28 PM #2
    ThePerfectHacker
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    Quote Originally Posted by robinpatrick View Post
    solve for x: log7(x+8) - log7(x-1) = log710
    Okay, use the fact,
    \log(a/b)=\log(a)-\log(b)
    Thus,
    \log_7 (x+8)-\log_7(x-1)=\log_7 10
    Becomes,
    \log_7 \left( \frac{x+8}{x-1} \right)=\log_7 10
    This logarithm function is one-to-one,
    \frac{x+8}{x-1}=\frac{10}{1}
    Thus, cross multiply
    x+8=10(x-1)
    Thus,
    x+8=10x-10
    Thus,
    9x=18
    Thus,
    x=2
    Check solution and see that it works
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