Solve x=3^-2+2^-k/sqrt{2+5*4^-1}+5*frac{sqrt{9}}{6}

$$x = \frac { 3 ^ { - 2 } + 2 ^ { - k } } { \sqrt { 2 + 5 \cdot 4 ^ { - 1 } } } + 5 \cdot \frac { \sqrt { 9 } } { 6 }$$

Solve for k (complex solution)

$$k=-\log_{2}\left(\frac{-9\sqrt{13}\left(5-2x\right)-4}{36}\right)-\frac{2i\pi n_{1}}{\ln(2)}$$

$$n_{1}\in \mathrm{Z}$$

$$x\neq \frac{2\sqrt{13}}{117}+\frac{5}{2}$$

Solve for x

$$x=\frac{2\sqrt{13}}{13\times 2^{k}}+\frac{2\sqrt{13}}{117}+\frac{5}{2}$$