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Compare-2-2-2-and-3-3-3-Here-it-is-raised-1001-times-a-square-1000-times-a-cube-




Question Number 151549 by mathdanisur last updated on 21/Aug/21
Compare:  2^2^2^.^.^.          and     3^3^3^.^.^.       Here it is raised 1001 times a square,  1000 times a cube.
$$\mathrm{Compare}: \\ $$$$\mathrm{2}^{\mathrm{2}^{\mathrm{2}^{.^{.^{.} } } } } \:\:\:\:\:\mathrm{and}\:\:\:\:\:\mathrm{3}^{\mathrm{3}^{\mathrm{3}^{.^{.^{.} } } } } \\ $$$$\mathrm{Here}\:\mathrm{it}\:\mathrm{is}\:\mathrm{raised}\:\mathrm{1001}\:\mathrm{times}\:\mathrm{a}\:\mathrm{square}, \\ $$$$\mathrm{1000}\:\mathrm{times}\:\mathrm{a}\:\mathrm{cube}. \\ $$
Answered by MJS_new last updated on 21/Aug/21
x^x^x  =x^((x^x ))   2^((2^2 )) <3^3   a<b  2^a <3^b  ∀0<a≤b
$${x}^{{x}^{{x}} } ={x}^{\left({x}^{{x}} \right)} \\ $$$$\mathrm{2}^{\left(\mathrm{2}^{\mathrm{2}} \right)} <\mathrm{3}^{\mathrm{3}} \\ $$$${a}<{b} \\ $$$$\mathrm{2}^{{a}} <\mathrm{3}^{{b}} \:\forall\mathrm{0}<{a}\leqslant{b} \\ $$

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