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    Solve lnx=6/(5-lnx)

    I know the answer is e^2 or e^3 but I don't know how to get there. Any hints?
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    Multiply the equation by 5-lnx and you will have a quadratic in lnx.
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    5ln^2x-lnx=6 ?
    I tried solving that with no luck, I'll go over my working again though
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    Oh, basic factorising mistake, thanks
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    (5-\ln x)(\ln x) = 6
    5\ln x - (\ln x)^2 = 6

    Let y = ln x

    y^2 - 5y +6 = 0

    y=3, y=2

    \ln x = 3 , x = e^3
    \ln x = 2 , x = e^2


    Now I get neg rep for helping out ?
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    (Original post by sdgvrgverg)
    5ln^2x-lnx=6 ?
    I tried solving that with no luck, I'll go over my working again though
    Nope, it should be ln^2x - 5lnx + 6 = 0, then you could take lnx = y and you'll have y^2 - 5y + 6 = 0 which you could then factorise to give (y-2)(y-3) therefore the solutions are y = 3 and y = 2 which means lnx = 2 and lnx = 3 as y = lnx, then you do:

    lnx = 2
    x = e^2

    lnx = 3
    x = e^3

    =D
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    (Original post by CookieGhoul)
    (5-\ln x)(\ln x) = 6
    5\ln x - (\ln x)^2 = 6

    Let y = ln x

    y^2 - 5y +6 = 0

    y=3, y=2

    \ln x = 3 , x = e^3
    \ln x = 2 , x = e^2


    Now I get neg rep for helping out ?
    Because you're not supposed to give him the full solution.
 
 
 
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