Question

log x-1(12x-x^2-19)=3.

Answer 1

$log_{x-1}(12x-x^2-19)=3; ,\\ODZ:; left { {{12x-x^2-19 textgreater 0} atop {x-1 textgreater 0; ,; x-1ne 1}} right. ; left { {{(x-6+sqrt{17})(x-6-sqrt{17}) textless 0} atop {x textgreater 1; ,; xne 2}} right. \\xin (6-sqrt{17}, ;, 2)cup (2, ;, 6+sqrt{17})\\log_{x-1}(12x-x^2-19)=log_{x-1}(x-1)^3\\12x-x^2-19=x^3-3x^2+3x-1\\x^3-2x^2-9x+18=0\\x^2(x-2)-9(x-2)=0\\(x-2)(x^2-9)=0\\(x-2)(x-3)(x+3)=0\\x_1=-3; ,; x_2=2,; x_3=3\\x_1; ,; x_2notin ODZ\\Otvet:; ; x=3; .$