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 ight) left( 17+x ight) =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{-bpmsqrt{D}}{2a} = frac{-16pmsqrt{1296}}{2} = frac{-16pm36}{2}[/latex][latex]x_1 = 10,; x_2 = -26[/latex]ОДЗ: [latex] left { {{x - 1>0} atop {17+x>0}} ight. [/latex] [latex] left { {{x >1} atop {x>-17}} ight. [/latex]Ответе:[latex]x = 10[/latex]