Originally Posted by

**topsquark** According to what you have written, this is

$\displaystyle y = \frac{1000 \cdot 10^{2.806x^{-0.444 \cdot 11.08^{0.138 \cdot 4202463^{0.235 \cdot 5508000^{0.4}}}}}}{0.8515 \cdot 1000000}$

There is a way to solve for x but as far any practical calculation is concerned,

$\displaystyle z = 11.08^{0.138 \cdot 4202463^{0.235 \cdot 5508000^{0.4}}}$

is so large that

$\displaystyle x^{-0.444 \cdot z} \approx 1$

to some 1000 decimal places.

So effectively y is a constant function for any reasonable scale factor.

Edit: I suppose for completeness I should say that this equation is basically just

$\displaystyle y = a \left ( 10^{x^b} \right )$

so the solution would be

$\displaystyle \frac{y}{a} = 10^{x^b}$

$\displaystyle x^b = log \left ( \frac{y}{a} \right )$

$\displaystyle x = \left [ log \left ( \frac{y}{a} \right ) \right ] ^{1/b}$

-Dan