# An algebra problem by Hemanth K

**Algebra**Level 3

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

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

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

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

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