[tex]\log{3100}=\log{(100\times 31)}=\log{100}+\log{31}=\log{10^2}+\log{31}=
\\ =2\log{10}+\log{31}=2\times1+\log{31}=2+\log{31}
\\
\\ 2+\log{10}\ \textless \ 2+\log{31}\ \textless \ 2+\log{100}
\\ 2+\log{10}\ \textless \ 2+\log{31}\ \textless \ 2+\log{10^2}
\\ 2+\log{10}\ \textless \ 2+\log{31}\ \textless \ 2+2\log{10}
\\ 2+1\ \textless \ 2+\log{31}\ \textless \ 2+2\times 1
\\ 3\ \textless \ 2+\log{31}\ \textless \ 4[/tex]
