Question

graph the following logarithmic functions. which has a graph that decreases from left to right? (1 point) \\(\log_{3} x\\) \\(\ln x\\) \\(\log_{0.5} x\\) \\(\log_{-2} x\\)

Explanation:

To determine which logarithmic function decreases from left to right, we use the property of logarithmic functions \( y = \log_b x \):

• If \( b>1 \), the function is increasing (e.g., \( \log_3 x \), \( \ln x=\log_e x \) with \( e > 1 \)).
• If \( 0 < b < 1 \), the function is decreasing. For \( \log_{0.5} x \), \( b = 0.5 \) (where \( 0<0.5<1 \)), so it is decreasing.
• The function \( \log_{-2} x \) is not a valid logarithmic function because the base of a logarithm must be positive and not equal to 1.

Answer:

\( \boldsymbol{\log_{0.5} x} \) (corresponding to the option with \( \log_{0.5} x \))