The Difference Between Log and Natural LogDate: 8 Feb 1995 20:05:32 -0500 From: Anonymous Subject: Logarithms What is the difference between log and natural log? I am having problems with this, so please help me. Date: 8 Feb 1995 22:29:17 -0500 From: Dr. Sydney Subject: Re: Logarithms Hello! Suppose we have y = lnx; z = log t where ln is log base e and log is log base 10. Then these equations are equivalent to the following statements: e^y = x; 10^z = t Sometimes it is easier to think of logs in these terms instead! So, the difference is in the base -- ln has base e, log has base 10. Hope this helps! Write back if you have any more problems! Sydney, "dr. math" Date: 8 Feb 1995 23:41:01 -0500 From: Elizabeth Weber Subject: Re: Logarithms Now, what is e? Well, it's real name is Euler's number, and it's equal to 2.71828182...... But why would we care enough about e to have a special kind of logarithm for it? Well, for some reason it's a number that pops up all over the place (Especially when you learn calculus). For instance, if you draw the graph of 1/x, the area between this graph and the x-axis between x=0 and x=1 is the natural log of x.....but that's calculus. But you don't have to be using calculus to run into e occasionally. e shows up in statistics and in growth problems. You've learned about interest, right? If you have a hundred dollars, and the interest rate is 10%, you soon have $110, and the next time interest is figured out you're adding another 10% of $110, so you'll get $121, and so on... What happens when the interest is being computed continuously (all the time)? You might think you'd soon have an infinite amount of money, but actually, you have your initial deposit times e to the power of the interest rate times the amount of time: (interest rate x time) (deposit) (e) And e just naturally shows up again in growth problems, and in some statistics problems too, which is why we bother giving the natural log a special name. Elizabeth, a math doctor |
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