2^x^x^x =2^(√2) x=?


Question and Answers Forum

All Questions Topic List
Algebra Questions
Previous in All Question Next in All Question
Previous in Algebra Next in Algebra
Question Number 192171 by mathlove last updated on 10/May/23

$2^{x^{x^{x}}} = 2^{\sqrt{2}}$ $x = ?$
Commented by Frix last updated on 11/May/23

$2^{x^{x^{x}}} = 2^{(x^{(x^{x})})}$ $\ln 2^{x^{x^{x}}} = \ln 2^{\sqrt{2}}$ $x^{x^{x}} = \sqrt{2}$ $x^{x} \ln x = \frac{\ln 2}{2}$ $We can only approximate$
Commented by mathlove last updated on 11/May/23

$o k$
	Answered by josemate19 last updated on 10/May/23

	$l n 2 x^{x^{x}} = l n 2^{\sqrt{2}}$ $x^{x} l n 2 x = \sqrt{2} l n 2$ $x^{x} = \frac{\sqrt{2} l n 2}{l n 2 x}$ ${l n x}^{x} = l n (\frac{\sqrt{2} l n 2}{l n 2 x})$ $x l n x = l n (\frac{\sqrt{2} l n 2}{l n 2 x})$ $x = \frac{l n (\frac{\sqrt{2} l n 2}{l n 2 x})}{l n x}$ $x = \frac{l n (\frac{l n 2^{\sqrt{2}}}{l n 2 x})}{l n x}$
	Commented by Frix last updated on 11/May/23

	$Wrong .$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum