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Question Number 17989 by alex041103 last updated on 13/Jul/17

$$Solveforx$$$$x^{x^{x^{x^{....}}}}=4$$

Commented by alex041103 last updated on 13/Jul/17

$$justforfun$$

Commented by mrW1 last updated on 13/Jul/17

$${\mathrm{x}}^4=4$$$$\mathrm{x}={}^4\sqrt{4}=\sqrt{2}$$

Commented by alex041103 last updated on 13/Jul/17

$$good$$

Commented by mrW1 last updated on 13/Jul/17

$${\left(\sqrt{2}\right)}^{{\left(\sqrt{2}\right)}^{{\left(\sqrt{2}\right)}^{(.....)}}}=?$$

Commented by mrW1 last updated on 13/Jul/17

$$2^{\frac{k}{2}}=k$$$$\Rightarrow \mathrm{k}=2\mathrm{or}4$$$$\mathrm{i}.\mathrm{e}.$$$${\left(\sqrt{2}\right)}^{{\left(\sqrt{2}\right)}^{{\left(\sqrt{2}\right)}^{(...)}}}=2\mathrm{or}4$$$$\mathrm{but}\mathrm{how}\mathrm{can}\mathrm{it}\mathrm{be}\mathrm{two}\mathrm{different}\mathrm{values}?$$

Commented by alex041103 last updated on 13/Jul/17

$$also-\sqrt{2}iasolution$$$${(-\sqrt{2})}^4={(-1)}^4{\left(\sqrt{2}\right)}^4=4$$

Commented by prakash jain last updated on 13/Jul/17

$$x^{x^{x^{\text{iddots}\mathrm{\infty }}}}=4$$$$\sqrt{2}\mathrm{is}\mathrm{not}\mathrm{a}\mathrm{valid}\mathrm{solution}.$$

Commented by alex041103 last updated on 13/Jul/17

$$True$$

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