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# Can anyone explain the difference between the logarithm of a product and the product of logarithms?

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10 years ago
 Can anyone explain the difference between the logarithm of a product and the product of logarithms? Logarithms really confuse me.  I need help Read 417 times 1 Reply

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10 years ago
 Well, for one thing, they are just different.The logarithm of a product is sort of much more simple than the product of logarithms. Why? Because if you have the logarithm of a product, then the following formula is true:ln (a*b) = (ln a) + (ln b)And if you have the product of logarithms: (ln a)*(ln b), you can't do anything with it The product of logarithm doesn't carry much meaning, it is just some expression. And the logarithm of a product makes much more sense. For example, in Physics there are lots of expressions like ln (something*something), but almost never (ln smth)*(ln smth).Well, that's not much, I've tried my best. The short answer is: they're just different, and it's easy to find an example when they are different. What I've tried is to give a somewhat bigger answer. As for me (personally, and I do have some experience), logarithm of a product is something "nice" and desirable, while product of logarithms is something "uncomfortable" )
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