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

log0.5x
logarithm subscript 0.5 baseline x

lnx

Answer 1

To determine which of the given logarithmic functions decreases from left to right, let's analyze the properties of each function:

1. \( \log_{-2}(x) \): This function is defined for \( x > 0 \) and is undefined for bases that are negative, so this function does not exist in the traditional sense.

2. \( \log_{2}(x) \): This is a logarithmic function with base 2. It is an increasing function, meaning that as \( x \) increases, \( \log_{2}(x) \) also increases.

3. \( \log_{0.5}(x) \): This function has a base of 0.5, which is less than 1. Logarithmic functions with bases less than 1 decrease as \( x \) increases. Thus, \( \log_{0.5}(x) \) is a decreasing function.

4. \( \ln(x) \): The natural logarithm, which has a base of \( e \) (approximately 2.718). This is also an increasing function.

Based on this analysis, the function that decreases from left to right is:

**\( \log_{0.5}(x) \)**, as it is the only function among the options provided that decreases as \( x \) increases.