Quoting Myrmidon

The reason you're getting 1.8384 for natlog(5) is because you don't have a semicolon after the third line. That is, the number 1.8384 is the value of xiplusone. A semicolon says 'continue to the next line and DON'T output the result of this line to the screen.' Without your S/C, it's just spitting out xiplusone after one iteration.

You should also be getting an error because you have no initial value of naturallog. How can naturallog = naturallog + 1 when naturallog never had a value to begin with? For all the program knows, naturallog is actually a string. Now, I'm not too keen on while loops, but I think the reason you don't get an error with natlog(5) is because 5-1.8384 is greater than 0.0001 (therefore the 'while' loop's end criteria are always met and it is being skipped entirely). Like I said, not to keen on while loops, so I might be reading this wrong (and I haven't reinstalled matlab since I formatted, so I can't check).

Your while loop is pretty shaky as it is. You NEED to change xi or xiplusone inside the loop, or the loop's end criteria will never be met - infinite loop issue. This should always be a criteria when you write a loop.

Now then:

1. Your while loop is not consistent with the stated problem. abs(xi-xiplusone) > 0.0001 should be the criteria. I have no idea what that xi >=1 is. Remember: while loops say "IF this criteria is true, RUN my loop. Then check back with me!" Therefore, IF abs(xi-xiplusone) < 0.0001, your loop will run, and mine will stop. IF abs(xi-xiplusone) > 0.0001, your loop will stop and mine will run.

2. To make matlab work properly, I think you actually need the value 'xiplusone' to be 'naturallog.' The way you've set up the function, it's going to return whatever is in the 'naturallog' variable as its 'answer.' According to your sequence, the 'answer' is supposed to be the last iteration of xi. Therefore naturallog needs to be the final iteration of xiplusone.

3. Move the while loop one line up. Add another line before the while loop that says 'naturallog = xiplusone' and another after that that says 'xi = xiplusone.' Now make your while loop evaluate abs(xi-naturallog).

That should be:

function naturallog=natlog(y)
xi=1;
naturallog = 10000; //this junk value ensures the loop will run at least once
while abs(xi-naturallog)>.0001
xiplusone=xi-1+y*exp(-xi); //This calculates xiplusone
naturallog = xiplusone; //this hides the value 'xiplusone' in 'naturallog'
xi = xiplusone; //This sets the stage for the next loop to calculate xiplustwo.
end

end

This is all off the top of my head, so someone correct me if I'm wrong.