Question

Log2/3 |x-2|>log2/3 6

Answer 1

Ответ:

(-6;0) или (0,6)

Пошаговое объяснение:

логарифм с основанием меньше 1 убывающая функция.

поэтому |x-2|<6

Согласно ОДЗ  х не равен 2.

0<х-2<6 или -6<х-2<0

(-6;0) или (0,6)

Answer 2

To solve the inequality $\log_{\frac{2}{3}} |x - 2| > \log_{\frac{2}{3}} 6$, you can start by recognizing that both sides of the inequality have the same logarithmic base, which is $\frac{2}{3}$. Therefore, you can drop the logarithmic base and work with the inner expressions:

$|x - 2| > 6$

Now, let's solve this inequality. To do that, we can break it into two cases:

Case 1: $x - 2 > 6$ In this case, the absolute value can be removed: $x - 2 > 6$

Add 2 to both sides: $x > 8$

Case 2: $x - 2 < -6$ In this case, the absolute value can be removed as well, but note that when you have a negative on the right side of an absolute value, it becomes positive on the left side: $x - 2 < -6$

Add 2 to both sides: $x < -4$

So, you have two sets of solutions:

1. $x > 8$
2. $x < -4$

To express the combined solution, you can use set notation:

$(- \infty, -4) \cup (8, +\infty)$

This means that the solution to the inequality is all real numbers less than -4 and all real numbers greater than 8.