Algebra

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how would you solve these two equations.

ln x + ln(x+1)=1

ln(x+5) = ln(x-1) - ln(x+1)

  • Algebra -

    put to work the properties of logs.

    ln x + ln(x+1) = 1
    ln(x(x+1)) = 1
    x(x+1) = e
    x^2 + x - e = 0
    then use the quadratic formula

    ln(x+5) = ln(x-1)/ln(x+1)
    ln(x+5) = ln((x-1)/(x+1))
    x+5 = (x-1)/(x+1)
    x^2+6x+5 = x-1
    x^2+5x+6 = 0
    ...

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