Question

(1/5)^x <=1/25 Розв'яжіть нерівність

Answer 1

$(\frac{1}{5})^x\leq \frac{1}{25}\\ \\ (\frac{1}{5})^x\leq (\frac{1}{5})^2$

Поскольку $0$, функция убывающая, то знак неравенства меняется на противоположный.

$x\ge 2$

Ответ: x ∈ [2;+∞).

Answer 2

Смотри.................

Answer 3

To solve the inequality (1/5)^x ≤ 1/25, we can follow these steps:

Step 1: Rewrite both sides of the inequality with the same base. Step 2: Apply the properties of exponents to simplify the inequality. Step 3: Solve for x.

Let's go through each step in detail:

Step 1: Rewrite with the same base (1/5)^x is equivalent to (5^(-1))^x, which can be simplified to 5^(-x).

Now the inequality becomes: 5^(-x) ≤ 1/25

Step 2: Apply properties of exponents To simplify the inequality further, we know that 1/25 is equal to 5^(-2) (since 1/25 = 5^(-2)).

The inequality becomes: 5^(-x) ≤ 5^(-2)

Step 3: Solve for x Now we have an inequality with the same base on both sides. In this case, we can compare the exponents:

-x ≤ -2

Next, we need to isolate x by multiplying both sides by -1, and when we do this, we must reverse the inequality:

x ≥ 2

The solution to the inequality is x ≥ 2.