Question

Log( основание=0,7)(x+5)<0

Answer 1

$log_{0.7}(x + 5) < 0 \\ log_{0.7}(x + 5) < log_{0.7}1 \\ x+ 5 > 1 \\ x > - 4$
удовлетворяет
ОДЗ:
х+5>0

Ответ: х€(-4;+∞)

Answer 2

The given inequality is a logarithmic inequality in the form of:

log_{0.7}(x+5) < 0

To solve this inequality, we can use the following steps:

Step 1: Find the domain of the logarithmic function. Since the base of the logarithm is 0.7, which is between 0 and 1, the argument (x+5) of the logarithmic function must be positive. Therefore, the domain of the function is x+5 > 0 or x > -5.

Step 2: Rewrite the inequality in exponential form. Using the definition of logarithms, we can rewrite the inequality as:

0.7^0 < x+5

Step 3: Simplify the inequality. 0.7^0 is equal to 1, so the inequality becomes:

1 < x+5

Subtracting 5 from both sides, we get:

-4 < x

Step 4: Check the solution. We need to check that the solution we found in step 3 satisfies the domain of the logarithmic function. Since the domain is x > -5 and our solution is x > -4, the solution satisfies the domain.

Therefore, the solution to the inequality log_{0.7}(x+5) < 0 is x > -4.