Finding number of operations

May 2014
1
0
United States
Hi, I'm working on some discrete math homework, and while I don't want anyone to do it for me, I am in desperate need of help in understanding what it is I'm supposed to be doing. The problem is:

What is the largest [FONT=MathJax_Math]n[/FONT] for which one can solve within one second a problem using an algorithm that requires [FONT=MathJax_Math]f[FONT=MathJax_Main]([FONT=MathJax_Math]n[FONT=MathJax_Main])[/FONT][/FONT][/FONT][/FONT] bit operations, where each bit operation is carried out in [FONT=MathJax_Main]10[FONT=MathJax_Main]−[FONT=MathJax_Main]4[/FONT][/FONT][/FONT] seconds, with these functions [FONT=MathJax_Math]f[FONT=MathJax_Main]([FONT=MathJax_Math]n[FONT=MathJax_Main])[/FONT][/FONT][/FONT][/FONT]?

The first one is is for log n, if anyone can help me by walking through this one step by step, I'm sure I can get through the rest. Or if you can even write a similar equation and show me how to solve that, I'm sure I can get it, I just seem to have NO idea where I'm going with it. Thanks in advance!
 

HallsofIvy

MHF Helper
Apr 2005
20,249
7,909
If it takes f(n) operations and each operation takes \(\displaystyle 10^{-4}\) (I assume that's what you mean by "10-4". If you can't use Latex, at least write 10^-4) seconds then it will take \(\displaystyle f(n)*10^{-4}\). Set that equal to 1 and solve for n:
if f(n)= ln(n) then \(\displaystyle ln(n)(10^{-4})= 1\) so that \(\displaystyle ln(n)= 10^4\) and \(\displaystyle n= e^{10^4}\).