e and ln are useful for describing many processes in the natural world and being able to integrate and differentiate functions involving them enables us to understand how things in the natural world behave.
http://betterexplained.com/articles/using-logs-in-the-real-world/
http://algebralab.org/lessons/lesson.aspx?file=Algebra_Exponents_e.xml
http://en.wikipedia.org/wiki/Natural_logarithm
Check the MyMaths lesson http://www.mymaths.co.uk/tasks/library/alevel/lib/loadLesson.asp?title=alevel/core3/IntegrationC3/integration9exlnx&taskID=2168
and check your understanding http://www.mymaths.co.uk/tasks/library/alevel/lib/loadTask.asp?title=alevel/core3/IntegrationC3/integration9exlnxOH&taskID=2168
Have a read around and find out where else lograthims and exponentials crop up... and post them here :)
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