log₁₃ (x²-2x)=log₁₃ (x²-24)
{x²-2x>0
{x²-24>0
{x²-2x=x²-24
x²-2x>0
x(x-2)>0
x=0 x=2
+ - +
------- 0 --------- 2 ---------
\\\ \\\\\
x∈(-∞; 0)U(2; +∞)
x²-24>0
(x-√24)(x+√24)>0
(x-2√6)(x+2√6)>0
x=2√6 x=-2√6
+ - +
--------- -2√6 ---------- 2√6 ------------
\\\\\ \\\\\\\\
x∈(-∞; -2√6)U(2√6; +∞)
х∈(-∞; -2√6)U(2√6; +∞)
x²-2x=x²-24
x²-2x-x²=-24
-2x=-24
x=-24 : (-2)
x=12
Ответ: 12.