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[latex]2^{x+1}+17\cdot 2^{-x} \leq 35\\\\2^{x}\cdot 2+\frac{17}{2^{x}}-35 \leq 0\\\\t=2^{x}\ \textgreater \ 0\; ,\; \; \; 2t+\frac{17}{t}-35 \leq 0\\\\ \frac{2t^2-35t+17}{t} \leq 0\; ,\; \; t\ne 0\\\\2t^2-35t+17=0\\\\D=35^2-4\cdot 2\cdot 17=1089\; ,\; \; \sqrt{1089}=33\\\\t_1=\frac{35-33}{4}=\frac{1}{2}\; ,\; \; t_2=\frac{35+33}{4}=17\\\\2(t-\frac{1}{2})(t-17) \leq 0\\\\(0)+++(\frac{1}{2})---(17)+++\\\\t\in [\, \frac{1}{2};17\, ]\; \; \to \; \; 2^{-1} \leq 2^{x} \leq 17\; \; \to \; \; \; \underline {-1 \leq x \leq log_217}[/latex]