  Let $[\, \cdot\,]$ be the floor function. In this paper we show that every
sufficiently large positive integer $N$ can be represented in the form
\begin{equation*} N=[p_1\log p_1]+[p_2\log p_2]+[p_3\log p_3], \end{equation*}
where $p_1,\, p_2,\, p_3$ are prime numbers. We also establish an asymptotic
formula for the number of such representations, when $p_1,\, p_2,\, p_3$ do not
exceed given sufficiently large positive number.
