Question

Log5 (x^{2} + 5x) = log5 (x^{2} + 9)

Answer 1

$log_{5}( {x}^{2} + 5x) = log_{5}( {x}^{2} + 9)$

В силу монотонного возрастания функции у = log_{a}[x] , где а > 1 , уравнение принимает вид:

${x}^{2} + 5x = {x}^{2} + 9 \\ \\ 5x = 9 \\ \\ x = \frac{9}{5} = 1.8$

удовлетворяет ОДЗ

ОТВЕТ: 1,8

Answer 2

x^2+5x=x^2+9

5x=9

x=9/5

Answer 3

To solve the equation $\log_5 (x^2 + 5x) = \log_5 (x^2 + 9)$, we can use the property of logarithms that states:

$\log_b(a) = \log_b(c)$ if and only if $a = c$.

So, in our equation, we have:

$x^2 + 5x = x^2 + 9$.

Now, we can solve for $x$:

$x^2 + 5x - (x^2 + 9) = 0$

$x^2 + 5x - x^2 - 9 = 0$

$5x - 9 = 0$

$5x = 9$

$x = \frac{9}{5}$.

Thus, the solution to the equation is $x = \frac{9}{5}$.