Question
Graph the following logarithmic functions. Which has a graph that decreases from left to right?(1 point) Responses log0.5x logarithm subscript 0.5 baseline x log−2x logarithm subscript negative 2 baseline x log2x logarithm subscript 2 baseline x lnx
Answers
GPT-4o mini
To analyze which of the given logarithmic functions decreases from left to right, let's consider the base of each logarithm:
1. **log₀.₅(x)**: This logarithm has a base less than 1, so it will decrease as \( x \) increases.
2. **log₋₂(x)**: The logarithm with a negative base is not defined in the realm of real numbers, so it cannot be graphed.
3. **log₂(x)**: This logarithm has a base greater than 1, so it will increase as \( x \) increases.
4. **ln(x)**: This is the natural logarithm with base \( e \) (approximately 2.718), which also increases as \( x \) increases.
Given this analysis, the only function that decreases from left to right is **log₀.₅(x)**.
So, the correct answer is:
- **log₀.₅(x)**
1. **log₀.₅(x)**: This logarithm has a base less than 1, so it will decrease as \( x \) increases.
2. **log₋₂(x)**: The logarithm with a negative base is not defined in the realm of real numbers, so it cannot be graphed.
3. **log₂(x)**: This logarithm has a base greater than 1, so it will increase as \( x \) increases.
4. **ln(x)**: This is the natural logarithm with base \( e \) (approximately 2.718), which also increases as \( x \) increases.
Given this analysis, the only function that decreases from left to right is **log₀.₅(x)**.
So, the correct answer is:
- **log₀.₅(x)**