1 + 2log32 The number N = 935 + log 2 when simplified reduces to : m2when in (1 + log; 2) (A) a prime number (B) an irrational number (C) a real which is less than log3 it (D) a real which is greater than log76 21 )

$$\begin{gathered} N\mathit{=}\frac{\mathit{1}\mathit{+}\mathit{2}\mathit{l}\mathit{o}{\mathit{g}}_{\mathit{3}}\mathit{2}}{{\mathit{(}\mathit{1}\mathit{+}\mathit{2}\mathit{l}\mathit{o}{\mathit{g}}_{\mathit{3}}\mathit{2}\mathit{)}}^{\mathit{2}}}\mathit{+}lo{g}_{\mathit{6}}^{\mathit{2}}\mathit{ }\mathit{2} \\ \mathit{=}\frac{\mathit{1}\mathit{+}\mathit{2}\mathit{ }\mathit{l}\mathit{o}{\mathit{g}}_{\mathit{3}}\mathit{2}\mathit{-}\mathit{l}\mathit{o}{\mathit{g}}_{\mathit{3}}^{\mathit{2}}\mathit{2}\mathit{-}\mathit{l}\mathit{o}{\mathit{g}}_{\mathit{3}}^{\mathit{2}}\mathit{2}}{ }\mathit{+}{\mathit{\left(}\frac{\mathit{l}\mathit{o}\mathit{g}\mathit{2}}{\mathit{l}\mathit{o}\mathit{g}\mathit{2}\mathit{+}\mathit{l}\mathit{o}\mathit{g}\mathit{3}}\mathit{\right)}}^{\mathit{2}} \\ \mathit{=}\frac{{\mathit{(}\mathit{1}\mathit{+}\mathit{l}\mathit{o}{\mathit{g}}_{{\mathit{3}}^{\mathit{2}}}\mathit{)}}^{\mathit{2}}\mathit{-}\mathit{l}\mathit{o}{\mathit{g}}_{\mathit{3}}^{\mathit{2}}\mathit{ }\mathit{2}}{{\mathit{(}\mathit{1}\mathit{+}\mathit{l}\mathit{o}{\mathit{g}}_{{\mathit{3}}^{\mathit{2}}}\mathit{)}}^{\mathit{2}}\mathit{ }}\mathit{ }\mathit{+}{\mathit{\left(}\frac{\mathit{l}\mathit{o}{\mathit{g}}_{{\mathit{3}}^{\mathit{2}}}}{\mathit{1}\mathit{+}\mathit{l}\mathit{o}{\mathit{g}}_{{\mathit{3}}^{\mathit{2}}}}\mathit{\right)}}^{\mathit{2}} \\ \mathit{=}\mathit{1}\mathit{-}\frac{\mathit{l}\mathit{o}{\mathit{g}}_{\mathit{3}}^{\mathit{2}}\mathit{ }\mathit{2}}{{\mathit{(}\mathit{1}\mathit{+}\mathit{l}\mathit{o}{\mathit{g}}_{{\mathit{3}}^{\mathit{2}}}\mathit{)}}^{\mathit{2}}} \\ \mathit{=}\mathit{1} \\ \mathit{\Rightarrow }\mathit{ }\boxed{\mathit{N}\mathit{=}\mathit{1}} \\ \mathit{3}\mathit{<}\pi \mathit{ }\mathit{ }\mathit{ }\mathit{ }\mathit{ }\mathit{ }\mathit{ }\mathit{ }\mathit{ }\mathit{ }\mathit{ }\mathit{ }\mathit{ }\mathit{ }\mathit{ }\mathit{ }\mathit{(}\mathit{\because }\pi \mathit{=}\mathit{3}\mathit{.}\mathit{14}\mathit{)} \\ lo{g}_{\mathit{3}}\mathit{ }\mathit{3}\mathit{<}lo{g}_{\mathit{3}}\pi \mathit{ }\mathit{ }\mathit{ }\mathit{\Rightarrow }N\mathit{<}lo{g}_{\mathit{3}}\pi \\ Option\mathit{ }c\mathit{ }is\mathit{ }correct\mathit{ } \\ \mathit{7}\mathit{>}\mathit{6} \\ lo{g}_{\mathit{7}}\mathit{7}\mathit{>}lo{g}_{\mathit{7}}\mathit{6} \\ \mathit{ }\mathit{\Rightarrow }N\mathit{>}lo{g}_{\mathit{7}}\mathit{6} \\ \mathit{o}\mathit{p}\mathit{t}\mathit{i}\mathit{o}\mathit{n}\mathit{ }\mathit{D}\mathit{ }\mathit{i}\mathit{s}\mathit{ }\mathit{c}\mathit{o}\mathit{r}\mathit{r}\mathit{e}\mathit{c}\mathit{t} \end{gathered}$$