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Logarithms question

  1. Oct 21, 2011 #1
    1. The problem statement, all variables and given/known data
    NEED HELP WITH THIS MATH PROBLEM: LOG3(X+3) + LOG3(X-1) = 1


    2. Relevant equations



    3. The attempt at a solution
    I SAID LOG3(X+3) + LOG3 (X-1)
    SIMPLIFIES TO LOG3(X+3)*(X-1) = 1
    I.E LOG3(X^2 +2X - 3) = 1
    THEN 3^1 = (X^2 +2X - 3)
    AND 0 = (X^2 +2X - 6)
    THEN USE THE QUADRATIC FORMULA TO FIND X AS {-2+/- 28^1/2}/2
    JUST NEED A SECOND OPINION TO SEE IF ITS CORRECT.
     
  2. jcsd
  3. Oct 21, 2011 #2

    ehild

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    The calculation is correct so far, but you have to investigate what root is solution of the original equation. Hint: is logarithm defined for negative numbers?


    ehild
     
  4. Oct 21, 2011 #3
    ok so logarithms are not defined by negative values hence the root for the original equation would have to be the positive value of x which would have been {-2 +[28^1/2]}/2 is that the final solution.
     
  5. Oct 21, 2011 #4

    ehild

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    Correct for the real logarithmic function.

    (Later you will learn about complex numbers and functions, and the complex logarithm is defined for negative numbers, too. )

    ehild
     
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