\frac{1}{8}\\\\(\frac{1}{2})^{x}>(\frac{1}{2})^3\\\\x<3\\\\x\in (-\infty ,3)\\\\\\ili\qquad (\frac{1}{2})^{x}>\frac{1}{8}\; \; \to \; \; 2^{-x}>2^{-3}\; \; \to \; \; -x>-3\; \; \to \; \; x<3" alt="(\frac{1}{2})^{x}>\frac{1}{8}\\\\(\frac{1}{2})^{x}>(\frac{1}{2})^3\\\\x<3\\\\x\in (-\infty ,3)\\\\\\ili\qquad (\frac{1}{2})^{x}>\frac{1}{8}\; \; \to \; \; 2^{-x}>2^{-3}\; \; \to \; \; -x>-3\; \; \to \; \; x<3" align="absmiddle" class="latex-formula">