How to Solve Using the Lambert W Function?

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  • เผยแพร่เมื่อ 20 ม.ค. 2025

ความคิดเห็น • 13

  • @Leivoso
    @Leivoso 23 วันที่ผ่านมา +1

    at 0:37 you assumed x≥0 in which there is no solution, but there is for x

  • @greatyeet2988
    @greatyeet2988 23 วันที่ผ่านมา +1

    If you just apply log on both sides you will end up with e^x/2 = x isn't that better simplified value?

    • @pandee6923
      @pandee6923 23 วันที่ผ่านมา

      how is that even a solution? x is on both sides, that's not a value. All you did was write the expression in a different way.

    • @greatyeet2988
      @greatyeet2988 23 วันที่ผ่านมา

      @pandee6923 my bad I am stupid

  • @DavidAndrew214
    @DavidAndrew214 24 วันที่ผ่านมา

    Thanks for the video. Are you saying that the Lambert function does not yield a real solution but there may still be one? I plugged y=x^2 and y=e^x into desmos and found an approximate solution

  • @pandee6923
    @pandee6923 23 วันที่ผ่านมา

    Or
    x^2 = e^x
    x^(1/x) = e^(1/2)
    1/x * ln x= 1/2
    e^ln(1/x) * ln x = 1/2
    -lnx * e^ln(1/x) = -1/2
    ln(1/x) * e^ln(1/x) = -1/2
    ln(1/x) = W(-1/2)
    ln x = -W(-1/2)
    x = e^[-W(-1/2)]

  • @greatyeet2988
    @greatyeet2988 23 วันที่ผ่านมา +1

    Why can't you solve using the basic logarithmic function?

    • @iskenderyahiaoui1844
      @iskenderyahiaoui1844 23 วันที่ผ่านมา

      you won't get any sort of linear equation you can't solve it in another way than the video

    • @greatyeet2988
      @greatyeet2988 23 วันที่ผ่านมา

      @iskenderyahiaoui1844 x = 2 log x if we apply log on both sides

    • @iskenderyahiaoui1844
      @iskenderyahiaoui1844 19 วันที่ผ่านมา

      @@greatyeet2988 yes okay and then ?
      You just wrote the équation differently it won't help at all u'll always endup using the w fonction

    • @greatyeet2988
      @greatyeet2988 10 วันที่ผ่านมา

      @@iskenderyahiaoui1844 then Diffrenciate on both sides

    • @iskenderyahiaoui1844
      @iskenderyahiaoui1844 10 วันที่ผ่านมา

      @@greatyeet2988 in the case of an équation x isn't a variable it's a constant
      By differentiating u'll get 0=0

  • @RonsherThirumaran
    @RonsherThirumaran 23 วันที่ผ่านมา

    answer is about -0.703467