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Math Help - (log) solve for x

  1. #1
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    (log) solve for x

    log3(x - 5) + log3(x + 3) = 2

    i need to solve for x. I know you can use the logx + logy = log(xy) but i can't get any further. help?
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  2. #2
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    log_3(x-5) + log_3(x+3) = log_3((x-5)(x+3)) = 2 = log_3(3^2)

    I used the fact that log_x(a) + log_x(b) = log_x(ab) and that log_x(x) = 1 and log_k(x^n) = n \cdot log_k(x)
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  3. #3
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    Quote Originally Posted by snypeshow View Post
    log3(x - 5) + log3(x + 3) = 2

    i need to solve for x. I know you can use the logx + logy = log(xy) but i can't get any further. help?
    First step: Determine the domain of this equation:

    x-5>0~\wedge~x+3>0~\implies~\boxed{x>5}

    And now proceed as Defunkt has described.
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