Question

1) log3 (x^2+7x+15)=1

Answer 1

Ответ:

Однозначно -4; -3

Понравился ответ? Жду лайк и 5 звезд! )))

Объяснение:

$log_{3} (x^{2} +7x+15)=1$

$log_{3} (x^{2} +7x+15)=log_{3} 3$

Это уравнение равносильно следующему:

$x^{2} +7x+15=3$

$x^{2} +7x+12=0$

По теореме Виета $x_{1} =-4 ; x_{2} =-3$

Оба корня входят в ОДЗ.

Answer 2

To solve the equation log₃(x² + 7x + 15) = 1, you'll need to rewrite it as an exponential equation and then solve for x.

The logarithmic equation log₃(x² + 7x + 15) = 1 can be rewritten in exponential form as:

3¹ = x² + 7x + 15

Now, simplify and solve for x:

3 = x² + 7x + 15

First, subtract 3 from both sides of the equation to isolate the quadratic term:

x² + 7x + 15 - 3 = 0

Now, simplify further:

x² + 7x + 12 = 0

This is a quadratic equation. To solve it, you can factor it or use the quadratic formula. In this case, it can be factored as:

(x + 3)(x + 4) = 0

Now, set each factor equal to zero and solve for x:

1. x + 3 = 0 x = -3

2. x + 4 = 0 x = -4

So, the solutions to the equation log₃(x² + 7x + 15) = 1 are x = -3 and x = -4.