Question

Log5(x+6)=log5(4x-3)

Answer 1

$\log_5(x+6)=\log_5(4x-3)$

Потенцируем уравнение

х+6=4х-3
Переносим неизвестные в правую часть
6=4х-3-х
6=4х-х-3
6=3х-3
Переносим свободные члены в левую часть
6+3=3х
9=3х
Делим обе части на 3
3=х
х=3.

Проверка подстановкой
$\log_5(3+6)=\log_5(4*3-3)$

$\log_59=\log_5(12-3)$

$\log_59=\log_59$

Получили тождество.

Значит 

Ответ: х=3.

Answer 2

Log((x+6)/(4x-3))=0

из свойств логарифма:
(x+6)/(4x-3) = 1
x+6-4x+3=0
x=3

Answer 3

To solve the equation log5(x+6) = log5(4x-3), you can use the property of logarithms that states that if two logarithms with the same base are equal, then their arguments must be equal as well. In this case, the base is 5.

So, you can set the arguments of the two logarithms equal to each other:

x + 6 = 4x - 3

Now, you can solve for x:

Subtract x from both sides:

6 = 3x - 3

Add 3 to both sides:

9 = 3x

Now, divide both sides by 3:

x = 3

So, the solution to the equation log5(x+6) = log5(4x-3) is x = 3.