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

log0.5x
logarithm subscript 0.5 baseline x

log−2x

1 answer

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

  1. \( \log_2 x \): This is the logarithm base 2. The graph of this function increases from left to right.

  2. \( \ln x \): This is the natural logarithm (base \( e \)). The graph also increases from left to right.

  3. \( \log_{0.5} x \): The base of this logarithm (0.5) is less than 1. Logarithmic functions with bases less than 1 decrease from left to right.

  4. \( \log_{-2} x \): Logarithms with negative bases are not defined for real numbers, so this function does not have a graph in the real number system.

Conclusion:

The function that has a graph that decreases from left to right is \( \log_{0.5} x \).