Question

demonstreaza ca 2^64<3^43

Answer 1

$2^{64}=2 \cdot 2^{63} =2 \cdot (2^3)^{21}=2 \cdot 8^{21}. \\ \\ 3^{43}=3 \cdot 3^{42}=3 \cdot(3^2)^{21}=3 \cdot 9^{21}. \\ \\ Deoarece~2\ \textless \ 3~si~8^{21}\ \textless \ 9^{21}~rezulta~ \boxed{2^{64}\ \textless \ 3^{43}} ~.$