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
log−2x
logarithm subscript negative 2 baseline x
log0.5x
Responses
log2x
logarithm subscript 2 baseline x
lnx
l n x
log−2x
logarithm subscript negative 2 baseline x
log0.5x
Answers
GPT-4o mini
To determine which of the given logarithmic functions decreases from left to right, we can analyze the behavior of each function:
1. **\( \log_2 x \)**: This function is logarithmic with a base greater than 1 (base 2). It increases from left to right.
2. **\( \ln x \)**: The natural logarithm function (base \( e \)) also increases from left to right.
3. **\( \log_{-2} x \)**: Logarithms with a negative base are not defined in the traditional sense for real numbers. This function does not exist for real \( x \).
4. **\( \log_{0.5} x \)**: This function has a base between 0 and 1 (base 0.5). Logarithmic functions with bases less than 1 decrease from left to right.
### Conclusion:
The function that decreases from left to right is **\( \log_{0.5} x \)**.
1. **\( \log_2 x \)**: This function is logarithmic with a base greater than 1 (base 2). It increases from left to right.
2. **\( \ln x \)**: The natural logarithm function (base \( e \)) also increases from left to right.
3. **\( \log_{-2} x \)**: Logarithms with a negative base are not defined in the traditional sense for real numbers. This function does not exist for real \( x \).
4. **\( \log_{0.5} x \)**: This function has a base between 0 and 1 (base 0.5). Logarithmic functions with bases less than 1 decrease from left to right.
### Conclusion:
The function that decreases from left to right is **\( \log_{0.5} x \)**.