Spain | A Nice Algebra Problem | Math Olympiad

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[@soniamariadasilveira7003]

Achei excelente, tenho um pouco de dificuldade com logaritmo

[@hongphuc9286]

*27^a=(3×9)^a=3^a×9^a*
*pt3^a+9^a-3^a×9^a=0*
*1+3^a-9^a=0*
*3^a={(-1+√[1^2-4(-1)(1)]}/(2×1)=(1+√5)/2*

[@prollysine]

Let u=3^a , we get , u^3+u^2-u=0 , u(u^2+u-1)=0 , u=0 , 0=3^a , ln(0)=a-ln3 ?? , ln(0) not defined , not a solu. ,
u^2+u-1=0 , u=(-1 |+/-| sqrt(1+4))/2 , u= (-1 + sqrt5)/2 , (-1 - sqrt5)/2 , / (-1 - sqrt5)/2 ,