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:

Step1: Recall Logarithmic Function Form

A logarithmic function has the form \( y = \log_b x \), where \( b>0, b
eq1 \) and \( x>0 \).

Step2: Analyze Each Option

• \( y = 0.25x \): This is a linear function (form \( y = mx + c \), here \( c = 0 \)), not logarithmic.
• \( y = x^{0.25} \): This is a power function (form \( y = x^n \)), not logarithmic.
• \( y=\log_{0.25}x \): This matches the logarithmic function form \( y = \log_b x \) with \( b = 0.25 \) (which is \(>0,

eq1\)).

• \( y=(0.25)^x \): This is an exponential function (form \( y = b^x \)), not logarithmic.

Answer:

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