Answer :
[tex]4^x-4^{-x}=24\\ \\4^x- \frac{1}{4^x} =24\\ \\ let\ 4^x=t\\ \\t- \frac{1}{t}=24\\ \Rightarrow t^2-1=24t\\ \Rightarrow t^2-24t-1=0\\ \Rightarrow t=12+ \sqrt{145}\\ (t=12- \sqrt{145}\ is\ ignored\ as\ 4^x\ can't\ be\ negative )\\ \\thus\ 4^x=12+ \sqrt{145} \\2^x= \sqrt{4^x} = \sqrt{12+ \sqrt{145}} [/tex]