A beautiful Stanford Exam Question | Nice Exponents Math Simplification

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  • Опубліковано 27 січ 2025

КОМЕНТАРІ • 4

  • @walterwen2975
    @walterwen2975 12 днів тому

    A beautiful Stanford Exam Question: (3ᵏ)(3ᵏ)(3ᵏ) = 36; k ,=?
    (3ᵏ)(3ᵏ)(3ᵏ)= 3³ᵏ = 36 = (3²)(2²), (3³ᵏ)/(3²) = 3³ᵏ⁻² = 2², log(3³ᵏ⁻²) = log2²
    3k - 2 = 2log₃2, 3k = 2 + 2log₃2, k = (2/3)(1 + log₃2)
    Answer check:
    k = (2/3)(1 + log₃2): 3k = 2 + 2log₃2 = 2log₃3 + 2log₃2 = 2log₃6 = log₃36
    3³ᵏ = 3^(log₃36) = 36; Confirmed
    Final answer:
    k = (2/3)(1 + log₃2) = (2/3)(1 + 0.631) = 1.087
    The calculation achieved on a smartphone with a standard calculator app

  • @RealQinnMalloryu4
    @RealQinnMalloryu4 13 днів тому

    {12+12+12}=36 12^12^12 1^1^12 1^2 (x ➖ 2x+1).

  • @veijolalli326
    @veijolalli326 14 днів тому

    3^k*3^k*3^k=36
    (3*3*3)^k=36
    27^k=36
    k*ln27=ln36
    k=ln36/ln27
    k=1.0872865023809716247330180762285

    • @veijolalli326
      @veijolalli326 14 днів тому

      Wow - this time I really learn something. Let me try
      3*k*3^k*3^k=36
      3^(3k)=36
      3^(3k-2)=4
      (3k-2)ln3=ln4
      3k-2=ln4/ln3
      3k=2+ln4/ln3
      k=(2+ln4/ln3)/3
      K=1.0872865023809716247330180762285
      same answer more steps😅