Brazil | Math Olympiad Exponential Challenge | How to Simplify Logarithims | Lambert W Function

[@ToanPham-wr7xe]

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[@SidneiMV]

64^x = x¹⁹²
(4^x)³ (x⁶⁴)³
4^x = x⁶⁴
x = 4^u
4^(4^u) = 4^(64u)
4^u = 64u
(1/64) = u4^(-u)
-1/64 = -u4^(-u)
(-uln4)e^(-uln4) = (-1/64)ln4
(-uln4)e^(-uln4) = (1/64)ln(1/4)
(-uln4)e^(-uln4) = (1/64)(1/4)ln(1/4)⁴
(-uln4)e^(-uln4) = (1/2⁸)ln(1/2⁸)
-uln4 = ln(1/28) = - 8ln2
2uln2 = 8ln2 => u = 4
x = 4^u => *x = 4⁴ = 2⁸ = 256*

[@Sergey_Moskvichev]

В Юникоде верхние буквенные символы тоже можно писать:
64ˣ=x¹⁹²; 4ˣ; 4ʸ; e⁻ᵘˡⁿ⁴.