# Factorial function intersections

How would you find the intersection between a factorial function and exponential function? ie work out:

$$x! = 2^x$$

Is it even possible ? As factorials only really work with integer values. When I plotted them on desmos, here was what was shown. I'm not sure if desmos just sorta made up the values between?

Thanks

• The gamma function where $\Gamma(n+1)=n!$ extends factoral to all numbers. $\Gamma(z)=\int_0^\infty x^{z-1}e^{-x}dx$. – herb steinberg Mar 21 at 16:26