Solving $n^a = x(n^x)$ for $x$ Okay. Let me just get straight to the point. I have a formula, $n^a = x(n^x)$. What I'm trying to do is make $x$ the subject of the formula. In other words, I want $x$ to express in terms of $a$ and $n$ only. It occured to me that this problem seemed rather impossible, but I'm no expert, you all are. So, here's my question. Is it possible, using any current mathematical hocus pocus, to express $x$ in terms of $a$ and $n$ only? If so, which area of maths do we have to get ourselves into? Can calculus help? 
Here are some facts and informations that I've gathered from this formula and feel free to correct me if I'm wrong:
1) $a \geq x$ (obviously) 
2) $a = x = 1$ (even more obvious) 
3) $n$ is a constant, $a$ is the independent variable and $x$ is the dependent variable. 
4) All value of $x$ are real numbers
5) When $a = 0$, $n$th root of $n = 1/x$
That's all the info I currently have. I really wish my question receives some decent answers. Thank you all for helping a poor little boy. I'm 15 in case you're wondering. I just realized I couldn't attach a picture because I don't have enough reputation :( 

One requires the use of the Lambert W function, which is required in step 3.  The solution is given as follows,
$$n^a=xn^x=xe^{x\ln(n)}\tag1$$
$$n^a\ln(n)=x\ln(n)e^{x\ln(n)}\tag2$$
$$W\left(n^a\ln(n)\right)=x\ln(n)\tag3$$

$$x=\frac{W\left(n^a\ln(n)\right)}{\ln(n)}\tag4$$

