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Muy interesante video muchas gracias por compartir 😊. Resolviendo con propiedades de logaritmos y cambio de variable. 😊❤😊.
So a=phi (the golden ratio) = about 1.618 and b=1/phi=phi-1=about 0.618.
1,618^ln(1,618)=1,260;0,618^ln(0,618)=1,260;1,618-0618=1 α=φ; b=φ-1
The first one is a=b or a=1/b in disguise. Trivial after that.
✌️👍😃😃👍✌️
ln²a = ln²b lnb = ± lna => b = a ∨ b = 1/ab = a => a - a = 1 [ not valid ]b = 1/a => a - 1/a = 1a² - a - 1 = 0a = (1 ± √5)/2a = (1 + √5)/2 => b = (-1 + √5)/2a = (1 - √5)/2 => b = (-1 - √5)/2
Muy interesante video muchas gracias por compartir 😊. Resolviendo con propiedades de logaritmos y cambio de variable. 😊❤😊.
So a=phi (the golden ratio) = about 1.618 and b=1/phi=phi-1=about 0.618.
1,618^ln(1,618)=1,260;
0,618^ln(0,618)=1,260;
1,618-0618=1 α=φ; b=φ-1
The first one is a=b or a=1/b in disguise. Trivial after that.
✌️👍😃😃👍✌️
ln²a = ln²b
lnb = ± lna => b = a ∨ b = 1/a
b = a => a - a = 1 [ not valid ]
b = 1/a => a - 1/a = 1
a² - a - 1 = 0
a = (1 ± √5)/2
a = (1 + √5)/2 => b = (-1 + √5)/2
a = (1 - √5)/2 => b = (-1 - √5)/2