Question 58555
<pre>
5) 	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:
log b  a=log-a/log-b
 
Using this formula, find log sqr 1000 . Round your answer to the hundredth's place.
Answer:  
Show work in this space.   

thanks Tine I am having the hardwst time with these could you give me some dirrection thanks?

log b  a=log-a/log-b is "saying" that: {{{log (b, (a)) = (log ((a)))/(log ((b)))}}}
{{{log ((sqrt("1,000")))}}}, without a base, denotes base 10. So, we get:
{{{highlight(log ((sqrt("1,000"))))}}} = {{{log (10, (sqrt("1,000")))}}} = {{{log (10, matrix(2,1, " ", ("1,000"^(1/2))))}}} = {{{(1/2)log (10, ("1,000"))}}} = {{{(1/2)(log (("1,000"))/log ((10)))}}} = {{{(1/2)(3/1)}}} = {{{3/2}}} = <font color =red><font size = 4><b>1.50</font></font></b></pre>