A Famous Equation, x^2 = 2^x - Cleve Moler on Mathematics and Computing
 

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A recent episode of the popular YouTube channel [URL="https://www.youtube.com/watch?v=ndA0sF_0Rwk&list=PU_SvYP0k05UKiJ_2ndB02IA&index=44"]"blackpenredpen"[/URL] is about solutions to the famous equation

x^2 = 2^x

You should be able to see two solutions yourself, x = 2 and x = 4, because 2^2 = 2^2 and 4^2 = 2^4.

This post is about a third solution.

Contents[URL="https://www.labfans.com/bbs/admincp/#97542339-a27e-498e-a9dd-a23ae459296e"]Two graphs[/URL][URL="https://www.labfans.com/bbs/admincp/#ad1efb2c-f8d0-43b1-af38-ce03c7f19077"]The negative solution[/URL][URL="https://www.labfans.com/bbs/admincp/#e6fbb1ca-5c9a-4f22-a112-f83dd9ab61b4"]Logarithm[/URL][URL="https://www.labfans.com/bbs/admincp/#cf21aff2-f714-4476-bbc8-850aaf98a28a"]LambertW[/URL][URL="https://www.labfans.com/bbs/admincp/#fe59b3a8-2f48-45a5-bed7-58498b31059e"]Many digits[/URL][URL="https://www.labfans.com/bbs/admincp/#1a414af5-cf18-4ea0-9602-36e5eb4c6370"]Fixed points[/URL][URL="https://www.labfans.com/bbs/admincp/#edf933d0-798c-4955-8914-92a34b5702c1"]Thanks[/URL][URL="https://www.labfans.com/bbs/admincp/#4a739d11-c23a-443e-93b3-c2f6a02c1861"]Code[/URL]Two graphsThe figure shows the graphs of x^2 and 2^x and



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