2⁻ˣ⁺²=6²ˣ⁻³=2²ˣ⁻³×3²ˣ⁻³,
2⁻ˣ⁺²⁻²ˣ⁺³=3²ˣ⁻³,
2⁻³ˣ⁺⁵=3²ˣ⁻³.
Take logs of each side:
(-3x+5)log(2)=(2x-3)log(3),
-3xlog(2)+5log(2)=2xlog(3)-3log(3),
5log(2)+3log(3)=2xlog(3)+3xlog(2),
log(32×27)=x(2log(3)+3log(2))=xlog(72),
x=log(864)/log(72)=1.581 approx.