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Question Number 151549 by mathdanisur last updated on 21/Aug/21

$$\mathrm{Compare}:$$$$2^{2^{2^{{.}^{{.}^{.}}}}}\mathrm{and}{3}^{3^{3^{{.}^{{.}^{.}}}}}$$$$\mathrm{Here}\mathrm{it}\mathrm{is}\mathrm{raised}1001\mathrm{times}\mathrm{a}\mathrm{square},$$$$1000\mathrm{times}\mathrm{a}\mathrm{cube}.$$

Answered by MJS_new last updated on 21/Aug/21

$$x^{x^x}=x^{\left(x^x\right)}$$$$2^{\left(2^2\right)}<3^3$$$$a<b$$$$2^a<3^b\mathrm{\forall }0<a⩽b$$

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