Question

Решить неравенство 0.8^x < 1

Answer 1

$0.8^x \ \textless \ 1 \\ 0.8^x \ \textless \ 0.8^0$
Так как y =  $0.8^x$ - убывающая функция (основание степени меньше 1), x > 0. 

Ответ: x > 0. 

Answer 2

To solve the inequality 0.8^x < 1, we need to isolate x on one side of the inequality. Let's go step by step:

1. Recall that any positive number raised to the power of 0 is equal to 1, so we can rewrite 1 as 0.8^0.

2. Therefore, the inequality becomes 0.8^x < 0.8^0.

3. Now, we know that 0.8^0 is equal to 1 (any number raised to the power of 0 is 1), so the inequality becomes 0.8^x < 1.

Now, we can solve the inequality:

0.8^x < 1

Since both sides of the inequality have the same base (0.8), we know that the inequality holds if and only if the exponent on the left side is less than the exponent on the right side. So, we have:

x < 0

Therefore, the solution to the inequality is x < 0. This means any real number x that is less than 0 will satisfy the inequality 0.8^x < 1.