Question

which of the following is a logarithmic function?
○ $y = 0.25x$
○ $y = x^{0.25}$
○ $y = \log_{0.25} x$
○ $y = (0.25)^x$

Explanation:

A logarithmic function has the form \( y = \log_b x \) (where \( b>0, b
eq1 \)). Let's analyze each option:

• \( y = 0.25x \) is a linear function (form \( y = mx + c \), here \( c = 0 \), \( m = 0.25 \)).
• \( y = x^{0.25} \) is a power function (form \( y = x^n \), here \( n = 0.25 \)).
• \( y=\log_{0.25}x \) matches the logarithmic function form \( y=\log_b x \) with base \( b = 0.25 \) (and \( 0.25>0, 0.25

eq1 \)).

• \( y=(0.25)^x \) is an exponential function (form \( y = a^x \), here \( a = 0.25 \)).

Answer:

\( y=\log_{0.25}x \) (the third option: \( y = \log_{0.25}x \))