Question

решить неравенство
${2}^{x + 1} + \frac{1}{2} - {2}^{x} < 5$
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Answer 1

$2^{x+1}+\frac{1}{2}-2^{x}<5\\\\2^{x+1}-2^{x}<5-\frac{1}{2}\\\\2^{x} (2-1)<4\frac{1}{2}\\\\2^{x}<\frac{9}{2}\\\\log_{2}2^{x}<log_{2}\frac{9}{2}\\\\x<log_{2}4,5\\\\Otvet:\boxed{x\in(-\infty;log_{2}4,5)}$