x-1,\; \; OOF:\; 2^{x-1}>0,x\in R\\\\2^{x-1}<(\frac{1}{2})^{x-1}\\\\2^{x-1}<2^{1-x}\\\\x-1<1-x\\\\2x<2\\\\x<1\\\\Otvet:\; x\in (-\infty,1)" alt="log_{\frac{1}{2}}{(2^{x-1})}>x-1,\; \; OOF:\; 2^{x-1}>0,x\in R\\\\2^{x-1}<(\frac{1}{2})^{x-1}\\\\2^{x-1}<2^{1-x}\\\\x-1<1-x\\\\2x<2\\\\x<1\\\\Otvet:\; x\in (-\infty,1)" align="absmiddle" class="latex-formula">