$$\\log_5\;\sqrt{17}\\\\
=log_5\;17^{0.5}\\\\
=0.5\times log_5\;17\\\\
=0.5\times \frac{log17}{log5}\\\\$$
(I used the change of base law)
$${\frac{{\mathtt{0.5}}{\mathtt{\,\times\,}}{log}_{10}\left({\mathtt{17}}\right)}{{log}_{10}\left({\mathtt{5}}\right)}} = {\mathtt{0.880\: \!187\: \!213\: \!861\: \!293\: \!8}}$$
.$$\\log_5\;\sqrt{17}\\\\
=log_5\;17^{0.5}\\\\
=0.5\times log_5\;17\\\\
=0.5\times \frac{log17}{log5}\\\\$$
(I used the change of base law)
$${\frac{{\mathtt{0.5}}{\mathtt{\,\times\,}}{log}_{10}\left({\mathtt{17}}\right)}{{log}_{10}\left({\mathtt{5}}\right)}} = {\mathtt{0.880\: \!187\: \!213\: \!861\: \!293\: \!8}}$$