Question: Logarithms:

a) Without Using a calculator, find log 10000 where log means log to the base of 10.

b) Most calculators have 2 different logs on them: log, which is based 10, and ln, which is based e. In computer science, digital computers are based on the binary numbering system which means that there are only 2 numbers available to the computer, 0 and 1. When a computer scientist needs a logarithm, he/she needs a log to base 2 which is not on any calculator. To find the log of a number to any base, we can use a conversion formula as shown here:
\[{{\log }_{b}}a=\frac{\log a}{\log b}\]
Using this formula, find \[{{\log }_{2}}10000\].