Is there any way to solve this without using a graphing calculator? Solve for $x$:
$$x=2^{8-2x}$$
Whenever I've seen solutions to this question, they have always been through plotting the two graphs and finding their intersection point. But, is there any other way to solve this (perhaps in a more algebraic way)?

Hint
When you have linear and exponential function in the same equation, then use Lambert W function defined as
$$e^{W(x)}W(x)=x$$
Your equation becomes
$$4^xx=256$$
which is equivalent to
$$e^{x\ln4}x\ln4=256\ln4$$
Can you continue from here?
