Bài 1 :
Tự bấm máy tính nhé!
Bài 2 :
\(25\le5.5^n\le125\)
\(\Leftrightarrow5^2\le5^{n-1}\le5^3\)
\(\Leftrightarrow\left[{}\begin{matrix}n-1=2\\n-1=3\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}n=3\\n=4\end{matrix}\right.\) \(\left(tm\right)\)
Vậy ...............
Bài 3 :
Ta có :
\(3.24^{100}=3.3^{100}.8^{100}=3^{101}.\left(2^3\right)^{100}=3^{101}.2^{300}\left(1\right)\)
Lại có :
\(4^{300}=\left(2.2\right)^{300}=2^{300}.2^{300}=2^{2.150}.2^{300}=\left(2^2\right)^{150}.2^{300}=4^{150}.2^{300}\left(2\right)\)
Từ \(\left(1\right)+\left(2\right)\Leftrightarrow3^{101}.3^{300}< 4^{150}.2^{300}\left(3^{101}< 4^{150}\right)\)
\(\Leftrightarrow4^{300}>3.24^{100}\)
\(\Leftrightarrow4^{300}+3^{300}-2^{300}>3.24^{100}\)