Infinite Exponents

Question

0

520

2

I never know how to do these types of questions:

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

Thanks!

Guest Feb 21, 2019

+6248

+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

0

Thanks!

Guest Feb 23, 2019

Rom · Answer 1 · 2019-02-22T11:29:05

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

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