which of the following is a logarithmic function?

$y = 0.25x$
$y = x^{0.25}$
$y = \log_{0.25} x$
$y = (0.25)^x$

Question

which of the following is a logarithmic function?

$y = 0.25x$
$y = x^{0.25}$
$y = \log_{0.25} x$
$y = (0.25)^x$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "direct_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Logarithmic Functions" ], "new_concepts": [], "current_concepts": [ "Logarithmic Functions" ] } ## Identify the mathematical form of a logarithmic function $$ y = \log_{b} x \quad (b > 0, \, b eq 1) $$ ## Evaluate the given options against the standard form $$ \begin{aligned} &y = 0.25x \quad \text{(Linear function)} \ &y = x^{0.25} \quad \text{(Power function)} \ &y = \log_{0.25} x \quad \text{(Logarithmic function with base } 0.25\text{)} \ &y = (0.25)^x \quad \text{(Exponential function)} \end{aligned} $$

(A) $y = 0.25x$

(B) $y = x^{0.25}$

(C) $y = \log_{0.25} x$

(D) $y = (0.25)^x$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Logarithmic Functions" ] }

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Question

Explanation:

Identify the mathematical form of a logarithmic function

Evaluate the given options against the standard form

Answer: