Question

Graph the following logarithmic functions. Which has a graph that decreases from left to right?(1 point)
Responses

\(\log_{0.5}x\)
logarithm subscript 0.5 baseline x

\(\ln x\)
l n x

\(\log_{-2}x\)
logarithm subscript negative 2 baseline x

\(\log_2x\)

Answer 1

To analyze the functions provided and identify which graph decreases from left to right, let’s examine each one:

1. **\(\log_{0.5}x\)**:
- This is a logarithm with a base less than 1. In general, logarithmic functions with bases less than 1 will decrease from left to right.
- Therefore, this function decreases.

2. **\(\ln x\)**:
- The natural logarithm (with base \(e\)) increases as \(x\) increases. Hence, this function increases.

3. **\(\log_{-2}x\)**:
- Logarithms with a negative base are not defined in the real number system. Thus, we cannot analyze this function graphically.

4. **\(\log_2x\)**:
- This is a logarithm with a base greater than 1. Functions with bases greater than 1 will also increase from left to right. Therefore, this function increases.

Based on this analysis, the function **\(\log_{0.5}x\)** is the only one that decreases from left to right.

**Answer: \(\log_{0.5}x\)**.