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Math Help - Solve Logarithmic Equation

  1. #1
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    Solve Logarithmic Equation

    I need help solving this logarithmic equation:

    <br />
2\log_{5}x - \log_{5}2 = \log_{5}(2x+6)<br />

    I tried "subtracting" the left side and then exponentiating everything with a 5 to cancel out the logs, but then I get to a prime polynomial. I'm stuck.
    Help is much appreciated
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  2. #2
    MHF Contributor red_dog's Avatar
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    Medgidia, Romania
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    Conditions: x>0 and 2x+6>0
    \Rightarrow x\in(0,\infty)
    The equation can be written as
    \log_5x^2-\log_52=\log_5(2x+6)\Leftrightarrow \log_5\frac{x^2}{2}=\log_5(2x+6)\Leftrightarrow \frac{x^2}{2}=2x+6
    Solving the quadratic we get x=-2 and x=6
    but only x=6 satisfy the conditions.
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