1. ## Finding an intersect

Hi guys,

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.

Details:
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.

KP

2. ## Re: Finding an intersect

Originally Posted by KPPnut
Hi guys,

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.

Details:
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.

KP
I would use a numerical method like Newtons.

I've got $\displaystyle x \approx 14.5785$

I don't know if this is a plausible value because I don't know the dimension of the variable x.

EDIT: There exists a 2nd solution at $\displaystyle x\approx 78.4131$ . Maybe this helps better.

3. ## Re: Finding an intersect

Originally Posted by earboth
I would use a numerical method like Newtons.

I've got $\displaystyle x \approx 14.5785$

I don't know if this is a plausible value because I don't know the dimension of the variable x.

EDIT: There exists a 2nd solution at $\displaystyle x\approx 78.4131$ . Maybe this helps better.
Yeah, the first answer is what I'm after! I've also managed to get Newton's method working for other test cases, same problem just different numbers. Thanks very much for your help!!!!

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....

4. ## Re: Finding an intersect

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)

5. ## Re: Finding an intersect

Originally Posted by BobBali
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)
Cheers for the quick answer. Not familiar with the abbreviation GDC, what does it stand for (it's going to be something obvious isn't it?).