Question

comparati: 4^19-2^36 si 3^28

Answer 1

$4^{19}-2^{36} = 2^{38}-2^{36} = 2^{36}\cdot (2^2-1) = 2^{36}\cdot 3\\ \\\\ 2^{36}\cdot 3\,\,\text{ cu }\,\,3^{28}\Big|:3\\ \\ 2^{36}\,\,\text{ cu }\,\,3^{27}\\ \\ (2^4)^{9}\,\,\text{ cu }\,\,(3^3)^9\\ \\ 16^9\,\,<\,\,\,27^9\\ \\ \Rightarrow \boxed{4^{19}-2^{36}<3^{28}}$