Question

Log 1/4 (x-1) ≤ 1христа ради

Answer 1

Log 1/4 (x-1) ≤ 1
log 1/4 (x-1) ≤ log 1/4 (1/4)
(x-1) ≥ (1/4)
(т.к. 1/4 < 1 знак поменяли)
х ≥ 0,25+1
х ≥ 1,25

Answer 2

To solve the inequality, we need to isolate the variable x on one side of the inequality sign. Here are the steps to do that:

Step 1: Move the logarithmic term to one side of the inequality:

Log 1/4 (x-1) ≤ 1

Logarithmic inequality can be converted into exponential inequality as below:

1/4^(1) ≤ x-1

Simplify:

1/4 ≤ x-1

Step 2: Add 1 to both sides of the inequality:

1/4 + 1 ≤ x

5/4 ≤ x

Therefore, the solution to the inequality is:

x ≥ 5/4

So the interval notation for the solution is [5/4, ∞).