I'm trying to find the intersect between a linear function and a power (fractal) function. I thought all this would require is a simple bit of algebra. I've since broken my and several friends' heads over it and we keep getting stuck.
linear function: 18886 -233.7*x
power function: 3052000*x^-1.972
Bit of background: They are functions that describe product size from a ball mill for grinding minerals.
So basically, what I'm trying to solve is:
18886-233.7*x = 3052000*x^-1.972
I've rewritten this as:
18886 = 3052000 / x^1.972 + 233.7*x
18886*x^1.972 = 3052000 + 233.7*x^2.972
18886*x^1.972 - 233.7*x^2.972 = 305200
80.183*x^1.972 -x^2.972 = 13059.481
And this is more or less where I get stuck. Hope it is correct to this point... Would be great if someone could help me out with this.
Cheers in advance!!!
Just out of curiosity though, is there actually a way of solving through normal algebra? Got half the office baffled by this seemingly simple problem....
Some equations, such as this, It isn't feasible to solve algebraically; (LHS) a linear equation on one side = (RHS) exponential equation on the other... I've tried doing this before using Logs and it doesn't work out...
Only way to do this is using a GDC. (x=14.6 and x=78.4)