approximately, i believe, the equation should be:
1.41^x+ln(x)=y
This equation starts at (0,1),
and at x= 30 it is about 29,963.
If your really determined to get it to equal exactly 30,000, then play
with the 1.41 and change it to
n^30=29,998.533
and you get
n = 1.4100569946559586271749047307593
So, the more exact equation would be
1.4100569946559586271749047307593^x+ln(x)=y
which has points (0,1)
and
(30,30000.010121254719662437295027903)
which is pretty close to 30,000
Finally,
if you want to be even more exact then change the 1.41 for:
n^30=30,000-log(30)
This should theoritically give you the exact answer.
After some though, it might be easier to just change the 1.41 for the
n you get from n^30=30,000-log(30), without simplifing the n:
My ability for solving for bases is not as good as it used to be, but
I think you would get something like
n=10^(log(30,000-log(30)))/30
So the equivelent final answers withought decimals should be
10^(log(30,000-log(30)))/30^x+ln(x)=y
or more simply:
n^x+ln(x)=y
where n=10^(log(30,000-log(30)))/30
I got his by using log base 10, for some reason i couldnt do it using
(ln), which I though would not make any difference.
bassically i used the "properties of logs"
mainly the 3rd found in http://www.purplemath.com/modules/logrules.htm
which allowed me to move the exponent down.
A final note, this looks a lot more like a parapolic curve then a
logorithimic curve, used "graph" in google, and used an online
graphing calculator.
I argue though that both things are the same parabolic (almost=too) logorithmic,
if you really want the logorithmic feel though, you could always just
invert it by, starting at (30, 30,000), and just inversing the
equation. |
