0, x>\frac{1}{7}, \\ \log_\frac{1}{2}(7x-1)=-3\log_\frac{1}{2}\frac{1}{2}, \\ 7x-1=(\frac{1}{2})^{-3}, \\ 7x-1=8, \\ 7x=9, \\ x=1\frac{2}{7};" alt="\log_\frac{1}{2}(7x-1)=-3, \\ 7x-1>0, x>\frac{1}{7}, \\ \log_\frac{1}{2}(7x-1)=-3\log_\frac{1}{2}\frac{1}{2}, \\ 7x-1=(\frac{1}{2})^{-3}, \\ 7x-1=8, \\ 7x=9, \\ x=1\frac{2}{7};" align="absmiddle" class="latex-formula">