Algebra-2

Question Analysis
This question involves determining whether the logarithmic function is increasing or decreasing.
The main focus is on understanding how the value of the logarithm’s base (specifically when the base is between 0 and 1) affects the function’s monotonicity (increasing/decreasing behavior).

Key Concept Explanation
For a logarithmic function :
If the base , the function is decreasing. This means as x increases (from 0 to infinity), the value of decreases.
If the base , the function is increasing.
Here, the base of is , which is between 0 and 1, so the function is decreasing.

Step-by-Step Solution
1. Identify the base of the function : .
2. Classify the base relative to 1: , which falls into the "decreasing function" category for logarithms.
Verify with key points to confirm:
When :