Question

Log1/6(5х-11)=log1/6(3+3х)

Answer 1

ОДЗ :

1) 5x - 11 > 0   ⇒   5x > 11     ⇒   x > 2,2

2) 3 + 3x > 0  ⇒   3x > - 3   ⇒    x > - 1

Окончательно : x ∈ (2,2 ; + ∞)

$log_{\frac{1}{6}}(5x-11)=log_{\frac{1}{6}}(3+3x)\\\\5x-11=3+3x\\\\5x-3x=3+11\\\\2x=14\\\\x=7\\\\7\in(2,2;+\infty)\\\\Otvet:\boxed{7}$

Answer 2

Ответ:x=7

Объяснение:

Приравниваем аргументы логарифмов и получаем:

5х-11=3+3x;

5x-3x=3+11;

2x=14;

x=14/2;

x=7.

Answer 3

To solve the equation log₁/₆(5x - 11) = log₁/₆(3 + 3x), we can start by applying the properties of logarithms. Specifically, we can use the property that if logₐ(b) = logₐ(c), then b = c.

Therefore, we have:

5x - 11 = 3 + 3x

Next, we can simplify the equation by combining like terms:

5x - 3x = 3 + 11

2x = 14

Finally, we isolate x by dividing both sides of the equation by 2:

x = 14/2

x = 7

Therefore, the solution to the equation log₁/₆(5x - 11) = log₁/₆(3 + 3x) is x = 7.