Logarithm as limit Wolfram's website lists this as a limit representation of the natural log:
$$\ln{z} = \lim_{\omega \to \infty} \omega(z^{1/\omega} - 1)$$
Is there a quick proof of this? Thanks

$\ln z$ is the derivative of $t\mapsto z^t$ at $t=0$, so
$$\ln z = \lim_{h\to 0}\frac{ z^h-1}h=\lim_{\omega\to \infty} \omega(z^{1/\omega}-1).$$
