



 
Hi Marsia, One way to see the relationship is to use a calculator. To make sure we are using the same calculator try the online calculator at http://www.globalrph.com/calc.htm I wanted a calculator with a log button (this is log base 10) a 10^x = 10^{x} button a ln button (this is log base e) and an e^x = e^{x} button. So try these examples
Try some other numbers and then repeat the examples using ln and e^x. What you should see is that if you start with a number x, find y = log(x) and then calculate 10^{y} your answer is x, the number you started with. Also backwards, if you start with a number s, find t = 10^{s} and then calculate log(t) your answer is s, the number you started with. Using mathematical notation what you have seen is
These facts are true regardless of which logarithm function you use, that is
The only possible problem is that when calculating b^{logb(x)} = x you must start with a positive x as the domain of the log function is all positive x. Penny
 


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