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e=x^(x)
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You are currently reading a thread in /sci/ - Science & Math
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Anonymous
e=x^(x) 2016-01-24 14:08:34 Post No. 7806862
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e=x^(x) Anonymous 2016-01-24 14:08:34 Post No. 7806862 [Report]
sci, how can I find x in this equation? e=x^(x) pic unrelated
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Anonymous 2016-01-24 14:14:28 Post No.7806871
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Anonymous 2016-01-24 14:14:28 Post No.7806871 [Report]
>you dont
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Anonymous 2016-01-24 14:18:47 Post No.7806877
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Anonymous 2016-01-24 14:18:47 Post No.7806877 [Report]
x^x = e^(log(x^x)) = e^(x·log(x))

=>

log(x) == 1/x

and now you gotta check the productlog
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Anonymous 2016-01-24 14:20:18 Post No.7806878
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Anonymous 2016-01-24 14:20:18 Post No.7806878 [Report]
why don't you just see where x^x=e in a graph?
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Anonymous 2016-01-24 14:28:26 Post No.7806895
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Anonymous 2016-01-24 14:28:26 Post No.7806895 [Report]
>>7806878
Too inexact
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Anonymous 2016-01-24 14:44:51 Post No.7806920
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Anonymous 2016-01-24 14:44:51 Post No.7806920 [Report]
>>7806862
[eqn] e=x^x \implies 1-x \ln (x) = 0 [/eqn] Then use Newton's method and you get that [math] x \approx 1.76 [/math] or if you don't like that then use Lamberts W-function then [eqn] x = e ^{W(1)} [/eqn]
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