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Question Number 151533 by mathdanisur last updated on 21/Aug/21

Compare: 2^2^2 and 3^3^3

$$\mathrm{Compare}: \\ $$$$\mathrm{2}^{\mathrm{2}^{\mathrm{2}} } \:\:\:\mathrm{and}\:\:\:\mathrm{3}^{\mathrm{3}^{\mathrm{3}} } \\ $$

Commented by Rasheed.Sindhi last updated on 21/Aug/21

3^3^3 =(2+1)^((2+1)^((2+1)) )

$$\mathrm{3}^{\mathrm{3}^{\mathrm{3}} } =\left(\mathrm{2}+\mathrm{1}\right)^{\left(\mathrm{2}+\mathrm{1}\right)^{\left(\mathrm{2}+\mathrm{1}\right)} } \\ $$

Commented by MJS_new last updated on 21/Aug/21

yes. but is 2^2^2 smaller or larger than (2+1)^((2+1)^((2+1)) ) ?

$$\mathrm{yes}. \\ $$$$\mathrm{but}\:\mathrm{is}\:\mathrm{2}^{\mathrm{2}^{\mathrm{2}} } \:\mathrm{smaller}\:\mathrm{or}\:\mathrm{larger}\:\mathrm{than}\:\left(\mathrm{2}+\mathrm{1}\right)^{\left(\mathrm{2}+\mathrm{1}\right)^{\left(\mathrm{2}+\mathrm{1}\right)} } ? \\ $$

Commented by MJS_new last updated on 21/Aug/21

seriously???

$$\mathrm{seriously}??? \\ $$

Commented by MJS_new last updated on 21/Aug/21

what do you think which is larger?

$$\mathrm{what}\:\mathrm{do}\:{you}\:\mathrm{think}\:\mathrm{which}\:\mathrm{is}\:\mathrm{larger}? \\ $$

Commented by mathdanisur last updated on 21/Aug/21

Sorry this no ⇑ I shared

$$\mathrm{Sorry}\:\mathrm{this}\:\mathrm{no}\:\Uparrow\:\mathrm{I}\:\mathrm{shared} \\ $$

Commented by MJS_new last updated on 21/Aug/21

yes, obviously. only people like you share questions like this one...

$$\mathrm{yes},\:\mathrm{obviously}.\:\mathrm{only}\:\mathrm{people}\:\mathrm{like}\:\mathrm{you}\:\mathrm{share} \\ $$$$\mathrm{questions}\:\mathrm{like}\:\mathrm{this}\:\mathrm{one}... \\ $$

Commented by Rasheed.Sindhi last updated on 22/Aug/21

Actually mathdanisur ser we can′t expect such obvious question by a senior member such as you, specially when he had asked some high level & hard questions before this one.(however I confess that many questions by you I liked very much, specially I liked variety in your questions!)

$${Actually}\:{mathdanisur}\:{ser}\:{we}\:{can}'{t} \\ $$$${expect}\:{such}\:{obvious}\:{question}\:{by} \\ $$$${a}\:{senior}\:{member}\:{such}\:{as}\:{you}, \\ $$$${specially}\:{when}\:{he}\:{had}\:{asked}\:{some}\: \\ $$$${high}\:{level}\:\&\:{hard}\:{questions}\:{before} \\ $$$${this}\:{one}.\left({however}\:{I}\:{confess}\:{that}\:{many}\:{questions}\right. \\ $$$${by}\:{you}\:{I}\:{liked}\:{very}\:{much},\:{specially} \\ $$$$\left.{I}\:{liked}\:{variety}\:{in}\:{your}\:{questions}!\right) \\ $$

Commented by Rasheed.Sindhi last updated on 22/Aug/21

You′re welcome!

$$\mathrm{You}'\mathrm{re}\:\mathrm{welcome}! \\ $$

Commented by mathdanisur last updated on 22/Aug/21

Thank you so much dear ser Rasheed.S

$${Thank}\:{you}\:{so}\:{much}\:{dear}\:{ser}\:{Rasheed}.{S} \\ $$

Commented by mathdanisur last updated on 22/Aug/21

Thank you very much, your solutions can be presented as usual

$$\mathrm{Thank}\:\mathrm{you}\:\mathrm{very}\:\mathrm{much},\:\mathrm{your}\:\mathrm{solutions} \\ $$$$\mathrm{can}\:\mathrm{be}\:\mathrm{presented}\:\mathrm{as}\:\mathrm{usual} \\ $$

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