log(x^2-8x+17)по осн 3 *log3 по осн x-3=1
Свойство логарифмов
log(x^2-8x+17)по осн 3 : log(х - 3) по осн 3 = 1
log(x^2-8x+17)по осн 3 = log(х - 3) по осн 3
log(x^2-8x+17)по осн 3 - log(х - 3) по осн 3 = 0
log(x^2-8x+17):(х-3) по осн 3 = log1 по осн 3
(x^2-8x+17):(х-3) = 1
x^2-8x+17 - х + 3 = 0
x^2 - 9x + 20 = 0
D = 81 - 4*20 = 81 - 80 = 1
x1 = (9 -1)/2 = 8/2 = 4
x2 = (9+1) /2 = 10/2 = 5