Do i still need to learn how to compute with logarithms?

As a means of simplifying arithmetic calculations logarithms are obsolete. Likewise is the slide-rule, a closely related device. However, the logarithm is still a very important and useful concept in mathematics. It will not go away.

I once heard a mathematics educator (of an age) say that logarithms and slide-rules should be mastered by all students so that they could continue their calculation when their batteries were dead. Although I recognize the importance of logarithms, I could not buy that rationale at all. That makes as much sense as maintaining a horse stable in case your car runs out of gas.

You should know that (for example) log 100 + log 1000 = log 100000 (and understand the reasoning behind it).
(assuming logs to the base 10).

I don't know if that counts as "compute with".

Yes. Your calculator does not think for you.