Question

Log7 (-2 x + 9)= 2 *

Answer 1

Ответ:

log7 (2 * x + 9) = log7 (x^2 + 5 * x - 1);

Приведем уравнение к линейному виду.

2 * x + 9 = x^2 + 5 * x - 1;

Перенесем все значения на одну сторону.

x^2 + 5 * x - 1 - 2 * x - 9 = 0;

x^2 + 3 - x - 1 - 9 = 0;

x^2 + 3 * x - 10 = 0;

Найдем дискриминант квадратного уравнения:

D = b2 - 4 * a * c = 32 - 4 * 1 * (-10) = 9 + 40 = 49;

Так как дискриминант больше нуля то, квадратное уравнение имеет два действительных корня:

x1 = (-3 - √49)/(2 * 1) = (-3 - 7)/2 = -10/2 = -5;

x2 = (-3 + √49)/(2 * 1) = (-3 + 7)/2 = 4/2 = 2;

Ответ: х = -5 и х = 2.

Answer 2

To solve the equation $\log_7(-2x + 9) = 2$, you need to isolate $x$. Here are the steps to solve it:

Step 1: Rewrite the equation without the logarithm:

$\log_7(-2x + 9) = 2$

This is equivalent to:

$-2x + 9 = 7^2$

Step 2: Calculate $7^2$:

$49$

So, the equation becomes:

$-2x + 9 = 49$

Step 3: Now, isolate $x$:

Subtract 9 from both sides of the equation:

$-2x = 49 - 9$

$-2x = 40$

Step 4: Finally, divide both sides by -2 to solve for $x$:

$x = \frac{40}{-2}$

$x = -20$

So, the solution to the equation $\log_7(-2x + 9) = 2$ is $x = -20$.