Question

Решить неравенство log_0,2 (x-1)>=log_0,2 2

Answer 1

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Answer 2

To solve the inequality log₀.₂(x-1) ≥ log₀.₂2, we need to use properties of logarithms to simplify and find the solution. Here are the steps to do that:

Step 1: Recall the logarithmic property that logₐ(b) = logₐ(c) if and only if b = c.

Step 2: Apply the property to our inequality, which means we set the arguments inside the logarithms equal to each other:

log₀.₂(x-1) = log₀.₂2

Step 3: Now, both sides of the equation have the same base, which is 0.₂. Therefore, we can drop the logarithm notation and simply equate the arguments:

x - 1 = 2

Step 4: Solve for x:

x = 2 + 1

x = 3

Step 5: Now, we need to check whether the solution is valid for the original inequality. Since we can't have a logarithm with a non-positive argument, we need to make sure that (x - 1) > 0.

x - 1 > 0 3 - 1 > 0 2 > 0

Since 2 is greater than 0, the solution x = 3 is valid.

Step 6: Finally, we need to determine the solution set for the inequality. Since we've only found one solution, x = 3, the solution set is:

{x | x = 3}