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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) = log2²3k - 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; ConfirmedFinal answer:k = (2/3)(1 + log₃2) = (2/3)(1 + 0.631) = 1.087The calculation achieved on a smartphone with a standard calculator app
{12+12+12}=36 12^12^12 1^1^12 1^2 (x ➖ 2x+1).
3^k*3^k*3^k=36(3*3*3)^k=3627^k=36k*ln27=ln36k=ln36/ln27k=1.0872865023809716247330180762285
Wow - this time I really learn something. Let me try3*k*3^k*3^k=363^(3k)=363^(3k-2)=4(3k-2)ln3=ln43k-2=ln4/ln33k=2+ln4/ln3k=(2+ln4/ln3)/3K=1.0872865023809716247330180762285same answer more steps😅
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
{12+12+12}=36 12^12^12 1^1^12 1^2 (x ➖ 2x+1).
3^k*3^k*3^k=36
(3*3*3)^k=36
27^k=36
k*ln27=ln36
k=ln36/ln27
k=1.0872865023809716247330180762285
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😅