Log3 (x - 1) + 2 log9 (17+x) = 7 + log1/3 9

[latex]log_3 (x - 1) + 2 log_9 (17+x) = 7 + log_{1/3} 9[/latex] [latex]log_3 (x - 1) + log_3 (17+x) = 7 - log_{3} 3^2[/latex] [latex]log_3 [(x - 1) *(17+x)] = 5[/latex] [latex]3^5 = (x - 1) *(17+x)[/latex] [latex]-243+ \left( x-1 \right) \left( 17+x \right) =0[/latex] [latex]-243+x 17+x^2-17-x=0[/latex] [latex]x^2+16 x-260 = 0[/latex] [latex]x_{1,2}= \frac{-b\pm\sqrt{D}}{2a} = \frac{-16\pm\sqrt{1296}}{2} = \frac{-16\pm36}{2}[/latex] [latex]x_1 = 10,\; x_2 = -26[/latex] ОДЗ: [latex] \left \{ {{x - 1>0} \atop {17+x>0}} \right. [/latex] [latex] \left \{ {{x >1} \atop {x>-17}} \right. [/latex] Ответе:[latex]x = 10[/latex]