[tex]\displaystyle\bf\\a)\\\\\left(\frac{1}{2}\right)^x=4\\\\\\2^{-x}=2^2\\\\-x=2~~\Big|\cdot(-1)\\\\\boxed{\bf~x=-2}\\\\\\b)\\\\\left(\frac{1}{2}\right)^x=2^{x-2}\\\\2^{-x}=2^{x-2}\\\\-x=x-2\\\\-2x=-2~~\Big|\cdot(-1)\\\\2x=2\\\\x=\frac{2}{2}\\\\\boxed{\bf~x=1}[/tex]