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$|L'(1,\chi)/L(1,\chi)|$

Let $\chi$ be a primitive Dirichlet character $\mod q$, $q>1$. Is there a neat, simple way to give a good bound on $L'(1,\chi)/L(1,\chi)$? Assuming no zeroes $s=\sigma+it$ of $L(s,\chi)$ satisfy $\...