Question

Log 1/3 (2x-6) > log 1/3 (x+4)

Answer 1

Ответ:

x ∈ (3;10)

Пошаговое объяснение:

$log_{1/3} (2x-6) > log_{1/3} (x+4)\\2x-6$   ОДЗ: 2х-6>0    x>3

                                                           x+4>0     x>-4

x ∈ (3;10)

Answer 2

Ответ:

(3; 10)

Пошаговое объяснение:

$logx_{\frac{1}{3}} (2x-6)>log_{\frac{1}{3}}(x+4)\\\\ 2x-6$

ОДЗ:

$1)2x-6>0\\2x>6\\x>3\\\\2)x+4>0\\x>-4$

Answer 3

To solve the inequality $\log_{\frac{1}{3}} (2x-6) > \log_{\frac{1}{3}} (x+4)$, we need to follow these steps:

Step 1: Understand the logarithmic property For the same base $b$, if $\log_b A > \log_b B$, then $A > B$. In our case, the base is $\frac{1}{3}$, so the inequality becomes $2x - 6 > x + 4$.

Step 2: Solve the linear inequality Subtract $x$ from both sides: $2x - x - 6 > 4$. Simplify: $x - 6 > 4$.

Step 3: Solve for $x$ Add 6 to both sides: $x > 10$.

So, the solution to the inequality $\log_{\frac{1}{3}} (2x-6) > \log_{\frac{1}{3}} (x+4)$ is $x > 10$.