Find $f(x)$ for $f'(x) = f(x) \ln(f(x))$ and $f(0) = 1$ $$f'(x) = f(x) \ln\big(f(x)\big)$$
$$f(0) = 1, \qquad  f(x) > 0$$
I am studying for finals on my own and this exercise is really bothering me because I can't seem to solve it. If I divide by $f(x)$ I get $\ln'f(x) = \ln f(x)$ but then I don't know what to do. Any help is appreciated! 

$$\frac{f'(x)}{f(x)}=\ln{f(x)}$$
$$ \frac{d\ln{f(x)}}{dx}=\ln{f(x)}$$
Call $g(x)=\ln(f(x))$
$$g'(x)=g(x)$$
$$g(x)=ce^{x}$$
