Question

Log 1/2 (7х-21) > log 1/2 (6х) решить неравенство, определить промежуток.

Answer 1

Решение представлено на фотографии

Answer 2

$log_{0,5}(7x-21) > log_{0,5}(6x)$

$log_{0,5}(7x-21) - log_{0,5}(6x) > 0$

$log_{0,5}(\frac{7x-21}{6x}) > 0$

$log_{0,5}(\frac{7x-21}{6x}) > log_{0,5}(1)$

$\frac{7x-21}{6x} < 1$

Знак поменялся, т.к. в основании дробь.

$\frac{7x-21}{6x} - 1 < 0$

$\frac{7x-21-6x}{6x} < 0$

$\frac{x-21}{6x} < 0$

Методом интервалов расставляем точки 21 и 0.

Ответом будет x∈(0;21).

Answer 3

To solve the inequality log base 1/2 (7x - 21) > log base 1/2 (6x), we can use the properties of logarithms. Specifically, the logarithm inequality property states that for any positive base "a" and positive numbers "b" and "c," if log base "a" (b) > log base "a" (c), then b > c.

So, we can rewrite the given inequality as an exponential inequality:

7x - 21 > 6x

Now, let's solve for x:

Subtract 6x from both sides:

7x - 6x - 21 > 0

Simplify:

x - 21 > 0

Add 21 to both sides:

x > 21

Now we have found the solution to the inequality: x > 21.

The interval notation for this solution is (21, +∞), which means all real numbers greater than 21 satisfy the inequality.