Recently I am thinking about this question:
Assume $x$ is real, $x\geq0$, $c$ is a positive constant number and $z$ is also a real constant between $3.5$ and $4$. Now there is a function: $ f(x)=\frac{x}{c+\frac{1}{1-\left(1+\frac{1}{zx}\right)^{-z}}}. $ I want to find whether there is an approximation for $f(x)$ when $x$ is between $\left[0.1, 10\right]$ by logarithm function, because I draw the figure and it looks like it... (So, I just guess...).
The reason I want to find an approximation is because the expression of $f(x)$ is complicated. And from the figure, it is really like a logarithm function near $x=1$.
Could you help me? I hope to discuss with you. Thank you in advance.
Can anyone help? ::>_<::