Question

log0.8(x-2)>log0.8(7-0.5x)

Answer 1

$log_{0.8} (x-2) \ \textgreater \ log_{0.8} (7-0.5x) \\\\ x-2\ \textgreater \ 0;x\ \textgreater \ 2 \\ 7-0.5x\ \textgreater \ 0; 0.5x\ \textless \ 7; x\ \textless \ 14 \\ x\in (2;14) \\\\ x-2\ \textless \ 7-0.5x \\ 1.5x\ \textless \ 9\\ x\ \textless \ 6 \\\\ x\in(2;6)$