200*2^(x/9)-1600*2^(x/18)=0
200⋅2x9−1600⋅2x18=0|:(−200)−2x9+8⋅2x18=0|+2x98⋅2x18=2x9|19x89x⋅2x18⋅9x=2x9⋅9x89x⋅212=21|:21289x=2121289x=21−1289x=212|8=2323⋅9x=212227x=21227x=12x=2⋅27x=54
First divide through by 200:
2^(x/9) - 8*2^(x/18) = 0
Divide through by 2^(x/18)
2^(x/18) - 8 = 0
Rewrite this as
2^(x/18) = 2^3
So we must have
x/18 = 3
Multiply through by 18
x = 54
.