Is there a continuous function for [math]\displaystyle f(x)=\sum_{n=1}^x\log n[/math]?
If [math]f(x)[/math] is a continuous function and [math]f (2x^2 -1) = 2xf(x)[/math] for all [math]x,[/math] how can I prove that [math]f(x) =0?[/math]