0 \: \: x < 40 \\ log_{x - 2}(40 - x) > 0 \\ 40 - x > 1 \\ x < 39 \\ x - 2≠1 \\ x≠3 \\ x - 2 > 0 \\ x > 2 \\ x\in(3;39) \\ log_{x - 2}(40 - x ) < 1 \\ 1)x - 2 > 1 \: \: \:;x > 3 \\ 40 - x < x - 2 \\ - 2x < 42 \\ x > 21 \\x\in(21; + \infty) \\ 2)0 < x - 2 < 1 \\ 2 < x < 3 \\ 40 - x > x - 2 \\ - 2x > 42 \\ x < 21 \\ x\in(2;3)" alt=" log_{2}( log_{x - 2}(40 - x) ) < 0 \\ odz \\ 40 - x > 0 \: \: x < 40 \\ log_{x - 2}(40 - x) > 0 \\ 40 - x > 1 \\ x < 39 \\ x - 2≠1 \\ x≠3 \\ x - 2 > 0 \\ x > 2 \\ x\in(3;39) \\ log_{x - 2}(40 - x ) < 1 \\ 1)x - 2 > 1 \: \: \:;x > 3 \\ 40 - x < x - 2 \\ - 2x < 42 \\ x > 21 \\x\in(21; + \infty) \\ 2)0 < x - 2 < 1 \\ 2 < x < 3 \\ 40 - x > x - 2 \\ - 2x > 42 \\ x < 21 \\ x\in(2;3)" align="absmiddle" class="latex-formula">
Объединяя промежутки с ОДЗ получаем промежуток :
