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What is the history, real world uses for logarithms, and profesions that would benefit from an understanding of logarithms

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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.
One thing to remember is that logarithms are used to solve exponentials.  There are plenty of "real world" problems that are exponentials.  Some examples are compounding interest annually (or some sort of time frame), population growth, carbon dating, and radioactive decay.  This should give you a start on why its important to learn about logarithms.