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eight in this class were gonna do a lot of manipulation of logarithms and exponential functions okay and some of these relationships were going to use a lot throughout the semester and what I want to do is help you understand them by applying them to some very simple applications so here I have a to the M times a to the N equals a to the M plus N okay this works for any base you might use the base e for natural logs you might use base 10 and then if you just have a log and you dont put the base below it youre in fine log base 10 so lets apply this is something we can understand okay I think everybody this room could do a hundred times a thousand so I could say ten squared times 10 cubed is equal to ten to the two plus three now lets check that out okay Im 10 squared is a hundred ten cubed is a thousand and ten to the two plus three is ten to the fifth which with five zeros is a hundred thousand in a hundred times a thousand is a hundred thousand now if I come and express this i