Question
Graph the following logarithmic functions. Which has a graph that decreases from left to right?(1 point)
Responses
log0.5 x
logarithm subscript 0.5 baseline x
ln x
l n x
log−2 x
logarithm subscript negative 2 baseline x
log2 x
Responses
log0.5 x
logarithm subscript 0.5 baseline x
ln x
l n x
log−2 x
logarithm subscript negative 2 baseline x
log2 x
Answers
GPT-4o mini
To determine which of the provided logarithmic functions decreases from left to right, we need to understand the behavior of each logarithmic function.
1. **\( \log_{0.5} x \)**: The logarithm with a base between 0 and 1, such as 0.5, is a decreasing function. As \( x \) increases, \( \log_{0.5} x \) decreases.
2. **\( \ln x \)**: The natural logarithm (base \( e \)) is an increasing function. As \( x \) increases, \( \ln x \) increases.
3. **\( \log_{-2} x \)**: Logarithms with a negative base are not defined in the context of real numbers; hence, this function is not valid.
4. **\( \log_{2} x \)**: The logarithm with base 2 is an increasing function. As \( x \) increases, \( \log_{2} x \) increases.
### Conclusion:
The only function that decreases from left to right is \( \log_{0.5} x \).
1. **\( \log_{0.5} x \)**: The logarithm with a base between 0 and 1, such as 0.5, is a decreasing function. As \( x \) increases, \( \log_{0.5} x \) decreases.
2. **\( \ln x \)**: The natural logarithm (base \( e \)) is an increasing function. As \( x \) increases, \( \ln x \) increases.
3. **\( \log_{-2} x \)**: Logarithms with a negative base are not defined in the context of real numbers; hence, this function is not valid.
4. **\( \log_{2} x \)**: The logarithm with base 2 is an increasing function. As \( x \) increases, \( \log_{2} x \) increases.
### Conclusion:
The only function that decreases from left to right is \( \log_{0.5} x \).