Question
Graph the following logarithmic functions. Which has a graph that decreases from left to right?(1 point)
Responses
log0.5x
logarithm subscript 0.5 baseline x
log−2x
logarithm subscript negative 2 baseline x
lnx
l n x
log2x
Responses
log0.5x
logarithm subscript 0.5 baseline x
log−2x
logarithm subscript negative 2 baseline x
lnx
l n x
log2x
Answers
GPT 3.5
To determine which graph decreases from left to right, we need to look at the base of the logarithmic function. The base determines the direction of the graph.
1. log0.5x: The base is 0.5, which is between 0 and 1. This means that the graph will decrease from left to right.
2. log−2x: The base is -2, which is less than 0. However, since it is negative, the graph will not decrease from left to right.
3. lnx: This is the natural logarithm with base e, which is approximately 2.718. The graph of lnx increases from left to right.
4. log2x: The base is 2, which is greater than 1. This means that the graph will increase from left to right.
Therefore, the logarithmic function log0.5x has a graph that decreases from left to right.
1. log0.5x: The base is 0.5, which is between 0 and 1. This means that the graph will decrease from left to right.
2. log−2x: The base is -2, which is less than 0. However, since it is negative, the graph will not decrease from left to right.
3. lnx: This is the natural logarithm with base e, which is approximately 2.718. The graph of lnx increases from left to right.
4. log2x: The base is 2, which is greater than 1. This means that the graph will increase from left to right.
Therefore, the logarithmic function log0.5x has a graph that decreases from left to right.