  Assume that $N$ is a sufficiently large positive number. In this paper we
show that for a small constant $\varepsilon>0$, the logarithmic inequality
\begin{equation*} \big|p_1\log p_1+p_2\log p_2+p_3\log p_3-N\big|<\varepsilon
\end{equation*} has a solution in prime numbers $p_1,\,p_2,\,p_3$.
