## Friday, September 23, 2011

### log theory reminder - pari / gp useful

When working with a scientific calculator that has log to base e and log to base 10 only, employ 'Change of Base' theory.

Change of Base - Wikipedia

Source: http://www.wikipedia.org/wiki/Logarithm#Change_of_base

Change of Base - questions rewritten:

If you know even a little about logs then you should be able to answer the following question:

What is log to base 10 of 1000?
The blindingly obvious answer is three.

Here are two additional ways of phrasing things to get an answer:
• To what power do we raise 10 so as to obtain 1000
• How many zeros in 1000

Assuming your calculator only does natural log (log to base e) use Change of base:

log to base 10 of 1000 is (log to base e (1000))/(log to base e (10)) = 3

Pari / GP - an example using x=1+1365*2^15

Pari / GP is a number theory program. It is designed for working Mathematicians / Number theorists, and is most useful to folks comfortable with Mathematical theory.

It is not designed, primarily, as a 'user friendly calculator replacement' for lay folks.

Now using x as given above - what is log to base 2 of x?