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in this lesson were going to focus on simplifying natural logs with e so lets start with the basics what is the natural log of one log of one is always zero a log can have any base it could be base 4 it can be base 10 it could be anything however when it has the base e a log becomes a natural log so natural logs only have base e and e is a number its like 2.718 something but thats e so now what is the natural log of e because the base is the same as e ln base e of e is one so the natural log of e is always equal to one make sure you know that by the way now what is the natural log of e raised to the seventh we could take the seven and move it to the front so this is seven lne and we know that lne is one so this is equal to seven now what about e raised to the ln 8 what is that equal to do you recall what 5 log base 5 of 9 is equal to since these are the same the answer is simply not the natural log has the base e and so these are the same and the answer is simply 8. now what about