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I never know how to do these types of questions:

 

\({\sqrt{x}}^{{\sqrt{x}}^{{\sqrt{x}}^{{.}^{{.}^{.}}}}}=2\)

 

Thanks!

 Feb 21, 2019

Best Answer 

 #1
avatar+4449 
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\(\text{the infinite power tower equals 2, so }\\ \sqrt{x}^{\sqrt{x}^{\sqrt{x}^{\dots}}} = (\sqrt{x})^2 = 2\\ x = 2\)

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 Feb 22, 2019
 #1
avatar+4449 
+1
Best Answer

\(\text{the infinite power tower equals 2, so }\\ \sqrt{x}^{\sqrt{x}^{\sqrt{x}^{\dots}}} = (\sqrt{x})^2 = 2\\ x = 2\)

Rom Feb 22, 2019
 #2
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Thanks!

 Feb 23, 2019

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