Solve {l}{35=3.1log_{2}(1+x)}{3.5y=0.31log_{2}(1+z)}{z=(94+1000)x}{m=y/1.6-1}{35*1.6=3.1log_{2}(1+n)}{h=n/x}

$$\left\{ \begin{array} { l } { 35 = 3.1 \log _ { 2 } ( 1 + x ) } \\ { 3.5 y = 0.31 \log _ { 2 } ( 1 + z ) } \\ { z = ( 94 + 1000 ) x } \\ { m = \frac { y } { 1.6 } - 1 } \\ { 35 \times 1.6 = 3.1 \log _ { 2 } ( 1 + n ) } \\ { h = \frac { n } { x } } \end{array} \right.$$

Solve for x, y, z, m, n, h

$$x=2048\times 2^{\frac{9}{31}}-1\approx 2503.527228042$$

$$y = \frac{31 \log_{2} {(2240512 \cdot 2 ^ {\frac{9}{31}} - 1093)}}{350} \approx 1.894112753$$

$$z=1094\left(2048\times 2^{\frac{9}{31}}-1\right)\approx 2738858.78747814$$

$$m=\frac{31\ln(2240512\times 2^{\frac{9}{31}}-1093)-560\ln(2)}{560\ln(2)}\approx 0.18382047$$

$$n=262144\times 2^{\frac{2}{31}}-1\approx 274131.932551636$$

$$h = \frac{262144 \cdot 2 ^ {\frac{2}{31}} - 1}{2048 \cdot 2 ^ {\frac{9}{31}} - 1} \approx 109.498282855$$