I'm having to right a research paper on logarithms and would like some help with it.
The most important use of logarithms is the base of calculator. The calculator works on the logarithmic base. For example, when you put 625X81 the calculator takes log of it and changes it to log(625X81) and using properties of log breakes it down to log625+log81=log(5^4)+log(3^4)=4log5+4log3 and wit built in table of logarithms it calculates the number.
Also, I know it is very usefull in space science calculations, since they work with extremely big numbers.