Question

(1/3)^(x-6)≤27 ______________________________

Answer 1

Ответ: [3;+Б)

Объяснение:

3^(6-x)<=3^3,   6-x<=3,   -x<=-3,  x>=3

Answer 2

To solve the inequality (1/3)^(x-6) ≤ 27, we need to isolate the variable on one side of the inequality sign. Let's go through the steps:

Step 1: Rewrite 27 as a power of 1/3: 27 = (3^3) = (3^3)^1 = 3^(3*1) = 3^3.

Step 2: Substitute 27 in the inequality with 3^3: (1/3)^(x-6) ≤ 3^3.

Step 3: Simplify both sides of the inequality: (1/3)^(x-6) ≤ 3^3 can be rewritten as (1/3)^(x-6) ≤ 3^(2+1).

Step 4: Apply the exponent properties: Since the bases are the same (3), we can equate the exponents. This gives us: x - 6 ≤ 2 + 1.

Step 5: Simplify the right side: x - 6 ≤ 3.

Step 6: Add 6 to both sides of the inequality to isolate x: x ≤ 3 + 6.

Step 7: Simplify the right side: x ≤ 9.

Therefore, the solution to the inequality (1/3)^(x-6) ≤ 27 is x ≤ 9.