Question

Answer 1

a) \(121\ge11^n\ge1\)

\(\Rightarrow11^2\ge11^n\ge11^0\)

\(\Rightarrow n\in\left\{2;1\right\}\)

b) \(49< 7^n< 343\)

\(\Rightarrow7^2< 7^n< 7^3\)

\(\Rightarrow n\in\varnothing\)

c) \(9< 9^n\le243\)

\(\Rightarrow3^2< 3^{2n}\le3^5\)

\(\Rightarrow2n\in\left\{3;4;5\right\}\)

\(\Rightarrow n=2\)

 

Answer 2

Answer 3

\(a,121\ge11^n\ge1\\ 11^2\ge11^n\ge11^0\\ 2\ge n\ge0\\ =>n=\left\{2;1;0\right\}\\ b,7^2< 7^n< 7^3\\ =>2< n< 3=>\varnothing\\ c,3^2< 3^{2n}\le3^5\\ 2< 2n\le5\\ =>n=\left\{2\right\}\)