Show that $\ln (x) \leq x-1 $ Show that $\ln (x) \leq x-1 $
I'm not really sure how to show this, it's obvious if we draw a graph of it but that won't suffice here. Could we somehow use the fact that $e^x$ is the inverse? I mean, if $e^{x-1} \geq x$ then would the statement be proved?

You may want to read the following note by E. R. Love:
The Mathematical Gazette Vol. 64, No. 427 (Mar., 1980), pp. 55-57 
