Finding number of operations

May 2014
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!


MHF Helper
Apr 2005
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 \(\displaystyle n= e^{10^4}\).