Question
Graph the following logarithmic functions. Which has a graph that decreases from left to right?(1 point)
Responses
log2x
logarithm subscript 2 baseline x
lnx
l n x
log0.5x
logarithm subscript 0.5 baseline x
log−2x
Responses
log2x
logarithm subscript 2 baseline x
lnx
l n x
log0.5x
logarithm subscript 0.5 baseline x
log−2x
Answers
GPT-4o mini
To determine which of the given logarithmic functions has a graph that decreases from left to right, let's analyze each function:
1. **\( \log_2 x \)**: This is the logarithm base 2. The graph of this function increases from left to right.
2. **\( \ln x \)**: This is the natural logarithm (base \( e \)). The graph also increases from left to right.
3. **\( \log_{0.5} x \)**: The base of this logarithm (0.5) is less than 1. Logarithmic functions with bases less than 1 decrease from left to right.
4. **\( \log_{-2} x \)**: Logarithms with negative bases are not defined for real numbers, so this function does not have a graph in the real number system.
### Conclusion:
The function that has a graph that decreases from left to right is **\( \log_{0.5} x \)**.
1. **\( \log_2 x \)**: This is the logarithm base 2. The graph of this function increases from left to right.
2. **\( \ln x \)**: This is the natural logarithm (base \( e \)). The graph also increases from left to right.
3. **\( \log_{0.5} x \)**: The base of this logarithm (0.5) is less than 1. Logarithmic functions with bases less than 1 decrease from left to right.
4. **\( \log_{-2} x \)**: Logarithms with negative bases are not defined for real numbers, so this function does not have a graph in the real number system.
### Conclusion:
The function that has a graph that decreases from left to right is **\( \log_{0.5} x \)**.