Graph the following logarithmic functions. Which has a graph that decreases from left to right?(1 point)

Question

Responses

log2x
logarithm subscript 2 baseline x

lnx
l n x

log−2x
logarithm subscript negative 2 baseline x

log0.5x

Answer 1

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 \( \log_{0.5} x \).