which statement is true?

$y = \log_{10} x$ is not a logarithmic function because the base is greater than 0.

$y = \log_{\sqrt{3}} x$ is not a logarithmic function because the base is a square root.

$y = \log_{1} x$ is not a logarithmic function because the base is equal to 1.

$y = \log_{\frac{3}{4}} x$ is not a logarithmic function because the base is a fraction.

Question

which statement is true?

$y = \log_{10} x$ is not a logarithmic function because the base is greater than 0.

$y = \log_{\sqrt{3}} x$ is not a logarithmic function because the base is a square root.

$y = \log_{1} x$ is not a logarithmic function because the base is equal to 1.

$y = \log_{\frac{3}{4}} x$ is not a logarithmic function because the base is a fraction.

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", "Logarithmic Domain" ] } ## Define logarithmic function base restrictions $$ y = \log_{b} x \implies b > 0 \text{ and } b eq 1 $$ ## Evaluate each statement against base restrictions $$ \begin{aligned} &\text{Option 1: } b = 10 > 0 \text{ and } 10 eq 1 \implies \text{Is a logarithmic function (False)} \ &\text{Option 2: } b = \sqrt{3} \approx 1.732 > 0 \text{ and } \sqrt{3} eq 1 \implies \text{Is a logarithmic function (False)} \ &\text{Option 3: } b = 1 \implies \text{Not a logarithmic function because } b = 1 \text{ (True)} \ &\text{Option 4: } b = \frac{3}{4} > 0 \text{ and } \frac{3}{4} eq 1 \implies \text{Is a logarithmic function (False)} \end{aligned} $$ ## Identify the correct statement $$ y = \log_{1} x \text{ is not a logarithmic function because the base is equal to 1.} $$

(A) $y = \log_{10} x$ is not a logarithmic function because the base is greater than 0.

(B) $y = \log_{\sqrt{3}} x$ is not a logarithmic function because the base is a square root.

(C) $y = \log_{1} x$ is not a logarithmic function because the base is equal to 1.

(D) $y = \log_{\frac{3}{4}} x$ is not a logarithmic function because the base is a fraction.

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

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QUESTION IMAGE

Question

Explanation:

Define logarithmic function base restrictions

Evaluate each statement against base restrictions

Identify the correct statement

Answer: