2011-II-39

Ans: C
Consider the option A,

$\begin{array}{cl}
& \log (1234^{1811}) \\
= & 1811 \log 1234 \\
= & 5~598.371~754
\end{array}$

Consider the option B,

$\begin{array}{cl}
& \log (2345^{1711}) \\
= & 1711 \log 2345 \\
= & 5~766.314~411
\end{array}$

Consider the option C,

$\begin{array}{cl}
& \log (3456^{1511}) \\
= & 1511 \log 3456 \\
= & 5~346.784~912
\end{array}$

Consider the option D,

$\begin{array}{cl}
& \log (7890^{1411}) \\
= & 1411 \log 7890 \\
= & 5~498.775~652
\end{array}$

Therefore, the least number is $3456^{1511}$.