# Finding x in terms of y for a complex equation

• Jun 14th 2012, 06:26 PM
ImaginaryMe
Finding x in terms of y for a complex equation
Hello everyone,

I'm having trouble with a pretty complicated equation to say the least and I was wondering if it were possible to solve for x in terms of y (x = ...).

The equation is the following:

y = 0.082 ArcTan[13.9(-0.0124+0.000139x)] -0.0281 ArcTan[24.7(0.0848+0.000139x)] -0.0539 Ln[4.12-0.00834x] +0.0182 Ln[19.1-0.0124x+0.0000695x^2] +0.00881 Ln[31.8+0.0848x+0.0000695x^2]

otherwise, if this one far too complicated, the arctans functions can be simplified to about 10^-4(x) (y intercept doesn't matter) with minimal loss, since all I need is about 250<x<520, so:

y = (-0.0539)ln(4.12-0.00834x)+0.0182ln(19.1-0.0124x+0.0000695x^2)+0.00882ln(31.8+0.0848x+0.000 0695x^2) + x*10^-4

Some software might probably be able to do this, but which one and how?

I hope this is mathematically possible, or if it can't be done algebraically then can it be done graphically?

[By the way, this equation is the result of the integration of:
0.0024185/[2500/(0.485x-6.331)-8.3168 ×10^(-11) x^4 ]
I used wolframalpha to solve it]

Help would be greatly appreciated, since I'm a little stumped right now. Thanks.