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Question Number 110725 by Study last updated on 30/Aug/20

$$x^{x^{x^{x^{...}}}}=2x=?$$

Answered by Her_Majesty last updated on 30/Aug/20

$$x^{x^{x^{...}}}=2$$$${lnx}^{x^{x^{...}}}=ln2$$$$x^{x^{x^{...}}}lnx=ln2$$$$but{x}^{x^{x^{...}}}=2\Rightarrow$$$$2lnx=ln2$$$$lnx=\frac{ln2}{2}$$$$x=\sqrt{2}$$

Answered by Dwaipayan Shikari last updated on 30/Aug/20

$$x^{x^{{xx}^{x^{x^{}}}}}=2$$$$x^2=2$$$$x=\sqrt{2}$$$$$$$$$$

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