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

Explanation:

Step1: Recall logarithmic - function form

A logarithmic function is of the form $y = \log_{a}x$, where $a>0,a\neq1$ and $x > 0$.

Step2: Analyze each option

• Option 1: $y = 0.25x$ is a linear function of the form $y=mx + b$ ($m = 0.25,b = 0$).
• Option 2: $y=x^{0.25}$ is a power - function of the form $y = x^{n}$ ($n = 0.25$).
• Option 3: $y=\log_{0.25}x$ is in the form of a logarithmic function with base $a = 0.25$.
• Option 4: $y=(0.25)^{x}$ is an exponential function of the form $y = a^{x}$ ($a = 0.25$).

Answer:

$y=\log_{0.25}x$