Question

ÁLGEBRA-TEORÍA DE EXPONENTE

Answer 1

$x=n^{n^{n^\vdots}}}=72+\sqrt{n}^{72+\sqrt{n}^{72+\sqrt{n}} ^{\vdots}}\\\\n^x=72+\sqrt{n}^x\\\\n^x-\sqrt{n}^x-72=0\\\\(\sqrt{n}^x)^2-\sqrt{n}^x-72=0\\\\(\sqrt{n}^x-9)(\sqrt{n}^x+8)=0\\\\n^{x/2}=9\\x^{1/2}=9\\x=81\\81=n^{81}\\\\\boxed{n=\sqrt[81]{81}}$