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Calculus

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Solve for x if 5+lnx=14/lnx.

  • Calculus - ,

    substitute y=ln(x) ....(1)
    to get
    5+y=14/y
    Solve the resulting quadratic equation in y.
    Note that the domain of ln(x) is ℝ+\0, reject the value of y≤0.
    Solve for x from (1) above.

  • Calculus - ,

    ok, so i got e^-7 and e^2
    does that mean i reject e^-7 because its less than or equal to 0?

  • Calculus - ,

    Your answers are correct,
    x=e-7 or x=e².

    In fact, the value of y in y=ln(x) can be anything in ℝ, so your answers are correct. The restriction for non-negative values are on x only. My apologies.

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