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India Math Olympiad question.

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[NaveenKushwaha-skki]

I am Indian
Brilliant explain❤❤
Do you know JEE mains and JEE advanced
And IIT

[RyanLewis-Johnson-wqxs]

(x/3)^(3+Log[10, x]=3*10^4 x=30 x=0.0001=1/10000 final answer

[SidneiMV]

(logx + 3)log(x/3) = 4 + log3
(logx + 3)(logx - log3) = 4 + log3

logx = u => x = 10ᵘ

(u + 3)(u - log3) - (4 + log3) = 0
u² + (3 - log3)u - 4(1 + log3) = 0

u = { log3 - 3 ± √[(3 - log3)² + 16(1 + log3)] }/2
u = { log3 - 3 ± √[(log3)² + 10log3 + 25] }/2
u = [log3 - 3 ± (log3 + 5)]/2

u = log3 + 1 = log30 ∨ u = -4

x = 10ᵘ
*x = 30 ∨ x = 10⁻⁴*