Question

Log3(x-2)<1Решить неравенство ​

Answer 1

ОДЗ : x - 2 > 0    ⇒   x > 2

$log_{3}(x-2)$

Answer 2

To solve the inequality log3(x-2) < 1, we need to find the range of values for x that satisfy the inequality. Here's the step-by-step solution:

Step 1: Remove the logarithm by rewriting the inequality in exponential form: 3^(log3(x-2)) < 3^1

Step 2: Simplify the right side of the inequality: 3^(log3(x-2)) < 3

Step 3: Since the base of the logarithm and the base of the exponential are the same, we can eliminate them, and the inequality becomes: x - 2 < 3

Step 4: Now, isolate x by adding 2 to both sides of the inequality: x < 3 + 2

Step 5: Final answer: x < 5

So the solution to the inequality is x < 5.