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oobleck why use a log table?
and, since sin300° = -sin60° = -√3/2
why use any tables?
well, I guess if you want an actual numeric value, then that would be
log |sin300°| = 1/2 log3 - log2 = -006247
ok, so now you have the log of |sin300°|. Try to find that value in your table.
You cannot, since log tables are always positive. But, if you find 0.06247 that will be log(1/sin300°), and you can see that
log 1.1547 = 0.06247
Now, having that you know that sin300° = -1/1.1547 = -0.8660
much less work to use trig tables or the Pythagorean Theorem.