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Let $\chi$ be a Dirichlet character modulo $q$, let $L(s, \chi)$ be theattached Dirichlet $L$-function, and let $L^\prime(s, \chi)$ denotes itsderivative with respect to the complex variable $s$. The main purpose of thispaper is to give an asymptotic formula for the $2k$-th power mean value of$\left|L^\prime/L(1, \chi)\right|$ when $\chi$ ranges a primitive Dirichletcharacter modulo $q$ for $q$ prime. We derive some consequences, in particulara bound for the number of $\chi$ such that $\left|L^\prime/L(1, \chi)\right|$is large.

An asymptotic distribution for $\left|L^\prime/L(1,\chi)\right|$