Algebra-2

Question Analysis
This question involves determining whether the basic logarithmic function is increasing or decreasing.
The main focus is on understanding how the function’s value changes as the input (x) increases, based on the value of the logarithm’s base.

Key Concept Explanation
For a logarithmic function :
If the base , the function is increasing. This means as x increases (from 0 to infinity), the value of also increases.
If , the function is decreasing (as x increases, decreases). Since the base of is 3 (which is greater than 1), the function is increasing.

Step-by-Step Solution
1. Identify the base of the function : .
2. Recall the rule for logarithmic function monotonicity (increasing/decreasing):
If , function is increasing; if , function is decreasing.
Compare the base to 1: , so the function follows the "increasing" rule.
Verify with key points:
When ,

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