how to do logarithms

Question

how to do logarithms

Answer 1

The logarithm is the power to which the base is raised to get a certain number.  What's that?  You want it in English?  Well, OK...

Let's start with base 10 logarithms.  (For this paragraph, "log" will mean base 10 log.)  If I say the log of 1,000 is 3, this means that 10 (the base) raised to the third power (log = 3) equals 1,000.  (Also note that the third root of 1,000 is 10.)  So log 100 = 2, log 1,000,000 = 6, etc.  Logs need not be integers; the log of 25,000 is approximately 4.39794 because 10 raised to the 4.39794 power is about 25,000.  Note that 4.39794 falls between 4 (log 10,000 = 4) and 5 (log 100,000 = 5).

Logs do not have to be base 10.  You will probably encounter natural logs (ln), in which the base is e (2.71828...).  For example  e squared is approximately 7.389.  So ln 7.389 = 2.