Logarithmic tables and logarithmic slide rules generally disappear in the late 70th and early 80th, with the spread of cheap portable electronic calculators.
Also computation with logarithms disappear from the school curriculum.
One cannot say however exactly when the last set of tables was published.
Some very similar tables are STILL in print.
I mean the tables for navigation, for example. They contain essentially logs of sines, and are designed to solve a spherical triangle. They are still published (and sold and bought) For example, here:
You may ask: who buys and uses them. The answer is a) hobbyists who like to do celestial navigation as it was done in the old days and b) those who justify their hobby by saying that they worry for backup for the Doomsday (when the batteries are dead/non available, GPS goes off, Internet not available, etc.)
I do not think anyone makes slide rules nowadays. But there is a large market for the old ones (see e-bay).