Question

Log3(2x-6)=log3(x+5)

Answer 1

Ответ:

11.

Пошаговое объяснение:

log_3(2x-6) = log_3(x+5)

ОДЗ:

{2х - 6 > 0,

{х + 5 > 0;

{2х > 6,

{х > - 5;

{х > 3,

{х > - 5;

(3; + ∞)

log_3(2x-6) = log_3(x+5)

2x-6 = x+5

2х - х = 6 + 5

х = 11.

Answer 2

To solve the equation $\log_3(2x-6) = \log_3(x+5)$, you can use the property of logarithms that states that if two logarithms with the same base are equal, then their arguments must also be equal. In this case, the base is 3. So, you can set the arguments equal to each other:

$2x - 6 = x + 5$

Now, you can solve for $x$:

Subtract $x$ from both sides:

$2x - x - 6 = x - x + 5$

Simplify:

$x - 6 = 5$

Add 6 to both sides:

$x - 6 + 6 = 5 + 6$

Simplify:

$x = 11$

So, the solution to the equation is $x = 11$.