Bài 4:
a) \(7^6+7^5-7^4=7^4\left(7^2+7-1\right)=7^4.55⋮55\)
b) \(81^7-27^9+3^{29}=3^{28}-3^{27}+3^{29}=3^{27}\left(3^2+3-1\right)=3^{26}.3.11=3^{26}.33⋮33\)
Bài 5:
a) \(\Rightarrow5^2< 5^n< 5^4\)
Do \(n\in Z\)
\(\Rightarrow n=3\)
b) \(\Rightarrow3^4>3^n\ge3^2\)
Do \(n\in Z\)
\(\Rightarrow n\in\left\{2;3\right\}\)
c) \(\Rightarrow2^4\le2^{3n}\le2^6\)
\(\Rightarrow3n\in\left\{4;5;6\right\}\)
Do \(n\in Z\)
\(\Rightarrow n=2\)
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