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Math Help - Logarithmic Equation Help

  1. #1
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    Logarithmic Equation Help



    Howdy friends --

    I'm in business calculus at a college in New Jersey and I recently was given this problem to solve on an online homework assignment. The question is to solve for x in terms of k and there is only one line for an answer.

    I have already tried submitting x=9^k and x=(9^k)-10, and neither are satisfactory to complete the problem.

    Please help!
    Many thanks,
    flk
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by funnylookinkid View Post


    Howdy friends --

    I'm in business calculus at a college in New Jersey and I recently was given this problem to solve on an online homework assignment. The question is to solve for x in terms of k and there is only one line for an answer.

    I have already tried submitting x=9^k and x=(9^k)-10, and neither are satisfactory to complete the problem.

    Please help!
    Many thanks,
    flk
    remember your formulas for summing logs, and taking the inverse of logarithms.

    \log_9 x + \log_9 (x + 10) = k

    \Rightarrow \log_9 [x(x + 10)] = k

    \Rightarrow 9^k = x(x + 10)

    this is a quadratic equation, use the quadratic formula to solve
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  3. #3
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    Thank you so much! It worked brilliantly. I never would have thought to set the equation up that way!
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  4. #4
    Math Engineering Student
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    Quote Originally Posted by Jhevon View Post
    \Rightarrow 9^k = x(x + 10)

    this is a quadratic equation, use the quadratic formula to solve
    Well from here we can save some of time by just completing the missing square.

    9^k+25=x^2+10x+25\implies9^k+25=(x+5)^2. The rest follows.
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