# The value of c for which conclusion of Mean value theorem holds for the function $f(x)= \log _e^x$ on the interval $[1,3]$ is
$\begin{array}{1 1} \log_3e \\ \log_e^3 \\ 2 \log _3 e \\ \frac{1}{2} \log _e^3 \end{array}$