  We consider two (natural) families of observables $O_k$ for systems with
dimension $d=3,4,5$: the spin observables $S_x$, $S_y$ and $S_z$, and the
observables that have mutually unbiased bases as eigenstates. We derive tight
entropic uncertainty relations for these families, in the form
$\sum_kH(O_k)\geqslant\alpha_d$, where $H(O_k)$ is the Shannon entropy of the
measurement outcomes of $O_k$ and $\alpha_d$ is a constant. We show that most
of our bounds are stronger than previously known ones. We also give the form of
the states that attain these inequalities.
