Question

Log3 (x^2+6) = log3 5x Проверку сделайте

Answer 1

Log3(x^2+6)=log 3 5x
x^2 +6-5x=0
x^2 -5x+6=0
D=(-5)^2- 4*6=25-24=1
x1=(5+1)/2=6/2=3
x2=(5-1)/2=4/2=2
ответ 2 ; 3

Answer 2

$log_3(x^2 + 6)=log_3(5x)\\ x^2 +6=5x \\ x^2 - 5x+6=0 \\ D = 25 - 24 =1\\\\ x_1=\frac{5+1}{2}=3 \\\\ x_1=\frac{5-1}{2}=2$
Проверка
1) x = 2
$log_{3}( {2}^{2} + 6) = log_{3}(10) \\ log_{3}(10) = log_{3}(10)$
2) x = 3
$log_{3}( {3}^{2} + 6) = log_{3}(15) \\ (15) log_{3}(15) = log_{3}(15)$