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? 發問於 Science & MathematicsMathematics · 6 年前

How do I solve log x + log (x-15)=2 ?

I don't understand how to set up this problem: How do I solve log x + log (x-15)=2

2 個解答

相關度
  • Tomp
    Lv 7
    6 年前
    最愛解答

    Note that one property of logarithms is that

    log(a) + log(b) = log(ab)

    for all logarithmic bases.

    Now assuming that by log you are referring to base 10, since without the subscript, it is implied.

    But

    log(x) + log(x - 15) = 2

    log(x(x - 15)) = 2

    x(x - 15) = 10²

    x² - 15x - 100 = 0

    x = (15 ± √((-15)² - 4*1*(-100)))/(2*1)

    = (15 ± √(225 + 400))/2

    = (15 ± √(625))/2

    = (15 ± 25)/2

    Since log(a) is undefined for a ≤ 0.we must have that

    x = (15 + 25)/2

    ie

    x = 20

  • 6 年前

    I got lost looking at that. Is that the quadratic formula?

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