200*2^(x/9)-1600*2^(x/18)=0

200*2^(x/9)-1600*2^(x/18)=0

\(\begin{array}{|rcll|} \hline 200\cdot 2^{\frac{x}{9}}-1600\cdot 2^{\frac{x}{18}} &=& 0 \quad & | \quad : (-200) \\ -2^{\frac{x}{9}}+8\cdot 2^{\frac{x}{18}} &=& 0 \quad & | \quad + 2^{\frac{x}{9}} \\ 8\cdot 2^{\frac{x}{18}} &=& 2^{\frac{x}{9}} \quad & | \quad 1^{\frac{9}{x} }\\ 8^{\frac{9}{x} }\cdot 2^{\frac{x}{18}\cdot {\frac{9}{x} }} &=& 2^{\frac{x}{9}\cdot {\frac{9}{x} }} \\ 8^{\frac{9}{x} }\cdot 2^{ \frac{1}{2} } &=& 2^{1 } \quad & | \quad : 2^{ \frac{1}{2} } \\ 8^{\frac{9}{x} } &=& \frac{ 2^{1} } {2^{ \frac{1}{2} }} \\ 8^{\frac{9}{x} } &=& 2^{1-\frac{1}{2} } \\ 8^{\frac{9}{x} } &=& 2^{ \frac{1}{2} } \quad & | \quad 8 = 2^3\\ 2^{\frac{3 \cdot 9}{x} } &=& 2^{ \frac{1}{2} } \\ 2^{\frac{27}{x} } &=& 2^{ \frac{1}{2} } \\\\ \frac{27}{x} &=& \frac{1}{2} \\ x &=& 2\cdot 27 \\ \mathbf{ x } & \mathbf{=} & \mathbf{54} \\ \hline \end{array}\)

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

.