A Nice Algebra Problem | Math Olympiad | A Nice Exponential Equation

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  • Опубліковано 17 січ 2025

КОМЕНТАРІ • 23

  • @JohnMooreVlogs
    @JohnMooreVlogs Місяць тому +1

    This was a neat little problem. I didn't imagine the process for solving it would be so complex at first glance. This was my first time seeing the Lambert W function. Thanks for taking the time to share it.

    • @SALogics
      @SALogics  Місяць тому

      You are most welcome! ❤

  • @ZendenSus
    @ZendenSus Місяць тому +4

    Also, we can say that both sides are 2 functions. The first function is exponential. The second is direct proportion function. The first function decreases, since the base is less than 1, and the second function increases because it is positive. Both of these functions intersect at one point and by selection we can find that it is 2

    • @SALogics
      @SALogics  Місяць тому +2

      Very nice! ❤

  • @aravindhnagarathinam
    @aravindhnagarathinam День тому +1

    👍👍👍

    • @SALogics
      @SALogics  День тому

      Thanks for liking! ❤

  • @walterwen2975
    @walterwen2975 Місяць тому +4

    Math Olympiad: (1/2)ˣ = x/8; x =?
    (1/2)ˣ = 1/(2ˣ) = x/8, x(2ˣ) = 8 = 2(4) = 2(2²); x = 2
    Answer check:
    x = 2: (1/2)ˣ = (1/2)² = 1/4, x/8 = 2/8 = 1/4; Confirmed
    Final answer:
    x = 2

    • @SALogics
      @SALogics  Місяць тому +1

      Very nice! ❤

  • @David_Lloyd-Jones
    @David_Lloyd-Jones Місяць тому +4

    2, by inspection.

    • @SALogics
      @SALogics  Місяць тому +1

      Very nice! ❤

  • @greatkabeer9306
    @greatkabeer9306 Місяць тому +3

    Took 10 minutes for just 30 seconds problem 😅

    • @SALogics
      @SALogics  Місяць тому +1

      Sorry for inconvenience! ❤

  • @garygornak
    @garygornak Місяць тому +2

    2

    • @SALogics
      @SALogics  Місяць тому +1

      Very nice! ❤

  • @carlosalbertoogliari1830
    @carlosalbertoogliari1830 Місяць тому +3

    Quanta sofisticação. Problema morre onde x.2^x = 2.2^2 logo x = 2.
    Enrabação de mosquito.

  • @obbyistguywhodoessomeguides
    @obbyistguywhodoessomeguides Місяць тому +1

    wdym i just used the good ol’ guess and check method and found it’s just 2

    • @SALogics
      @SALogics  Місяць тому +1

      Very nice! ❤

  • @CRAZY-M4U
    @CRAZY-M4U Місяць тому +1

    Kua hall hai

    • @SALogics
      @SALogics  Місяць тому +1

      I am fine, How are you?

  • @pspprabhat
    @pspprabhat 19 днів тому +1

    8(2^-×)=×
    =>8=×.2^×
    =>W{× ln2.e^ln2(×)}
    =W{2ln2.e^ln2(2)}
    =>×ln2=2ln2
    =>×=2