Pre-Calc

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Can someone show me how to do this please. I am stuck.


find a number x such that
e^2x – 12e^x =13

  • Pre-Calc -

    Substitute y=e^x to get a quadratic equation:
    y²-12x+13=0
    Solve for y.
    Substitute the values of y=e^x into the original equation to make sure that all the roots are feasible/defined.
    See also previous example:
    http://www.jiskha.com/display.cgi?id=1291874924

  • Pre-Calc -

    let e^x = t
    then
    e^2x – 12e^x =13 becomes
    t^2 - 12t - 13 = 0
    (t-13)(t+1) = 0
    t = 13 or t = -1

    then e^x = 13 or e^x = -1
    x = ln 13 or x = ln(-1)
    but in ln(a) a > 0

    so x = ln 13

  • oops -

    I slipped in the sign of the transformed equation. Instead of
    y²-12x+13=0
    it should read
    y²-12x-13=0

    Go with Reiny's solution.

  • Pre-Calc -

    Thank u both

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