Question
Graph the following logarithmic functions. Which has a graph that decreases from left to right?(1 point)
Responses
log−2x
logarithm subscript negative 2 baseline x
log2x
logarithm subscript 2 baseline x
lnx
l n x
log0.5x
Responses
log−2x
logarithm subscript negative 2 baseline x
log2x
logarithm subscript 2 baseline x
lnx
l n x
log0.5x
Answers
GPT-4o mini
To understand which of the given logarithmic functions decreases from left to right, let's analyze each function:
1. **log(-2)x**: This function is not defined for positive \( x \) since the logarithm with a negative base isn't defined in this context. Therefore, we can't plot it.
2. **log₂x**: This is a logarithm with a base of 2. The graph of log₂x increases from left to right. As \( x \) increases, \( log₂x \) increases.
3. **lnx**: This is the natural logarithm function. The graph of lnx also increases from left to right. As \( x \) increases, \( lnx \) increases.
4. **log₀.5x**: This has a base of \( 0.5 \) (which is less than 1). The graph of log₀.5x decreases from left to right. As \( x \) increases, \( log₀.5x \) decreases.
### Conclusion
The function that has a graph that decreases from left to right is **log₀.5x**.
1. **log(-2)x**: This function is not defined for positive \( x \) since the logarithm with a negative base isn't defined in this context. Therefore, we can't plot it.
2. **log₂x**: This is a logarithm with a base of 2. The graph of log₂x increases from left to right. As \( x \) increases, \( log₂x \) increases.
3. **lnx**: This is the natural logarithm function. The graph of lnx also increases from left to right. As \( x \) increases, \( lnx \) increases.
4. **log₀.5x**: This has a base of \( 0.5 \) (which is less than 1). The graph of log₀.5x decreases from left to right. As \( x \) increases, \( log₀.5x \) decreases.
### Conclusion
The function that has a graph that decreases from left to right is **log₀.5x**.