A nice exponential equation to solve| Math Olympiad #maths #matheolympiad

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[Emerson_Brasil]

In this type of content looking for roots of this type of equation, it is good to make it clear that you are looking for roots of whole numbers, if they exist.

[Emerson_Brasil]

It is important to note that this type of expression is so common in many math videos, but it never mentions that there are other non-integer real roots. A root is x≈1.011134481871269.

[SidneiMV]

4^(x²) = x¹²⁸
4^(x²) = (x²)⁶⁴

x²ln4 = 64lnx²
(1/x²)ln(x²) = (1/64)ln4
(1/x²)ln(x²) = (1/32)ln2
(1/x²)ln(1/x²) = (1/32)ln(1/2)

(1/x²)ln(1/x²) = (1/2⁵)(1/2³)8ln(1/2)
(1/x²)ln(1/x²) = (1/2⁸)ln(1/2⁸)

1/x² = 1/2⁸ => *x = ± 2⁴ = ± 16*