Math Olympiad | Wonderful Exponential Problem | VIJAY Maths

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[@elmer6123]

Learn to recognize Golden Ration problems and solution is trivial
φ^2+φ-1=0 has positive root (√5-1)/2 and Φ^2-Φ-1=0 has positive root (√5+1)/2
Substitute φ=9^(-x) into the given equation and rearrange to φ^2+φ-1=0.
Thus, 9^x=1/φ=Φ=(√5+1)/2 and x=lnΦ/ln9=0.21901

[@RealQinnMalloryu4]

{2x^2/162x^2+^22x^2/18x^2}=4x^4/180x^4 2^2x^2^2/2^90x^2^2 1^1x1^1/1^3^30x^1^1 /3^3^10 1^3^2^5x^1^3^2^1x 3^2x(x ➖ 3x+2).