I read this as:
(1) 4ˣ⁻¹+4ˣ⁺¹)/(17×2ˣ)=
4ˣ⁻¹(1+4²)/(17×2ˣ)=
4ˣ⁻¹(17)/(17×2ˣ)=
4ˣ⁻¹/2ˣ=2²ˣ⁻²⁻ˣ=2ˣ⁻².
(2) There seems to be a typo in this part, because 4t=t implies t=0.
If 3⁻ˣ=t, then log(3⁻ˣ)=log(t), -xlog(3)=log(t), x=-log(t)/log(3).
(4ˣ⁻¹+4ˣ⁺¹)/(17×2ˣ)=2ˣ⁻²=2^(-log(t)/log(3)-2)=
2^-((log(t)+log(9)/log(3))=2^-(log(9t)/log(3)).
If 3⁻ˣ=4t, (4ˣ⁻¹+4ˣ⁺¹)/(17×2ˣ)=2^-(log(36t)/log(3)).