Question 47675
<pre>
Logarithms:
a) 	Using a calculator, find log 1000 where log means log to the base of 10. 
Answer: 

b) 	Most calculators have 2 different logs on them: log, which is base 10, and ln, which is base 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 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:
 
Using this formula,a=log a/log b, find log2 1000 . Round your answer to the hundredth's place.
Answer:  
Show work in this space.  

<font color = red><font size = 4><b>b)</font></font></b> {{{highlight(log (2, ("1,000")))}}} = {{{log (("1,000"))/log ((2))}}} = {{{log ((10^3))/log ((2))}}} = {{{(3 log (10))/log ((2))}}} =  {{{3(1)/log ((2))}}} = {{{3/log ((2))}}} = <font color = red><font size = 4><b>9.97, approximately</font></font></b></pre>