In an effort to finally get to grips with logarithms (I had one related post today) I am looking for "real life" applications. Here is what I have found, and it astonishes me - they say that logarithms are great for multiplying two "big" numbers. Of course, for now let's pretend that we can't use calculator/computer to do the job. They suggest that multiplying 734 times 213 is much easier with log table, then, say, doing a straightforward multiplication on paper, or in the mind, even though the log usage doesn't give you a correct result.
Please, help me to understand why logs are more useful. Is it only because adding together smaller numbers "sounds" easier?
Also I will be truly grateful for your help on finding meaningful, mathematically correct real life applications of logarithms. Thank you very much!