An algebra problem by Hemanth K

If $a,n> 1$ , which of the following real numbers is larger in value?

$\begin{aligned} A &=& \log a + \log (a+1) + \cdots + \log(a+n-1) \\ B &=& (\log a + \log(a+n-1) ) \dfrac n2 \end{aligned}$