Solving a 'Germany' Math olympiad question

[@key_board_x]

4^(b) * 4^(b) = 80 [4^(b)]² = 80 4^(b) = ± √80 4^(b) = ± 4√5 → we keep only the positive value 4^(b) = 4√5 Ln[4^(b)] = Ln(4√5) b.Ln(4) = Ln(4√5) b = Ln(4√5) / Ln(4) b = [Ln(4) + Ln(√5)] / Ln(4) b = 1 + [Ln(√5) / Ln(4)]

[@AsadInternationalAcademy]

thank you so much dear

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[@juanjoalbertez103]

Absolutely amazing. 10/10.

[@AsadInternationalAcademy]

Wow, thanks!

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[@erwinn.1031]

4^(b)*4^(b)=80 4^(2b)=80 (2b)ln4=ln80 b=ln80/2*ln4

[@AsadInternationalAcademy]

thanks dear

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[@veijolalli326]

WRONG!!! - - - ln80/2*ln4 +++ ln80/2/ln4

[@AlexanderSemashkevich]

b=log80/2log4=(2log4+log5)/2log4=1+log5/4log2 b≈1+0.699/(4×0.301)≈1903/1204≈1.5805 Deviation is about 0.0001 4^(2×1.5805)≈4^3.161≈80.004

[@AsadInternationalAcademy]

beautiful solution

[@elektrotubbie]

Gracias. Muy entretenido.

[@AsadInternationalAcademy]

welcome dear

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[@angi3574]

MAL,PORQUE FALTA ROAVIA ...QUEDA LOG BASE 16 DE 80

[@AsadInternationalAcademy]

ok dear

[@AsadInternationalAcademy]

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[@hansgeorgschrey5168]

the solution shown is overly complicated - if you start writing the numbers in form of exponent of 2 you will be finished in seconds ... my personal view: not good for beginners !

[@AsadInternationalAcademy]

easy dear

[@AsadInternationalAcademy]

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[@adel7376]

(4^b)*(4^b)=(4^2*b)=(4^2)^b=16^b=80 d'ou ln(16^b)=ln80 b*ln16=ln80 b= ln80/ln16

[@AsadInternationalAcademy]

good dear

[@adel7376]

@@AsadInternationalAcademy 👍

[@veijolalli326]

4^(2b)=80 4^(2b-1)=20 4^(2b-2)=5 (2b-2)ln4=ln5 2b-2=ln5/ln4 2b=2+ln5/ln4 b=1+ln5/2/ln4 b=1.5804820237218405869675798573723

[@veijolalli326]

4^b*4^b=80 16^b=80 16^(b-1)=5 (b-1)ln16=ln5 b=1+ln5/ln16 b=1.5804820237218405869675798573723

[@AsadInternationalAcademy]

Good job, thanks dear

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[@joaosilverio8099]

Why 16*5 ?

[@AsadInternationalAcademy]

check out the lesson

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[@joaosilverio8099]

@@AsadInternationalAcademy thanks

[@robertoneves5406]

Não existe nenhum

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[@AsadInternationalAcademy]

here b

[@panini_checker]

Whoww...😮 Well..Using a calculator: * log(80) ≈ 1,9030899869919 * log(4) ≈ 0,6020599913279 * b ≈ (1.903... / 0.602...) / 2 * b ≈ 1,5804820237218

[@AsadInternationalAcademy]

ok dear

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