Question

which of the following is the inverse of \\(y = 12^x\\)?

\\(y = \log_{\frac{1}{12}} x\\)

\\(y = \log_{12} \frac{1}{x}\\)

\\(y = \log_x 12\\)

\\(y = \log_{12} x\\)

Explanation:

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<reasoning>

Swap variables to find the inverse

\[
x = 12^y
\]

Solve for y using logarithms

\[
y = \log_{12} x
\]
</reasoning>

<answer>
<mcq-option>(A) \(y = \log_{\frac{1}{12}} x\)</mcq-option>
<mcq-option>(B) \(y = \log_{12} \frac{1}{x}\)</mcq-option>
<mcq-option>(C) \(y = \log_{x} 12\)</mcq-correct>
<mcq-correct>(D) \(y = \log_{12} x\)</mcq-correct>
</answer>

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"question_type": "Multiple Choice",
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]
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Answer:

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</pre_analysis>

<reasoning>

Swap variables to find the inverse

\[
x = 12^y
\]

Solve for y using logarithms

\[
y = \log_{12} x
\]
</reasoning>

<answer>
<mcq-option>(A) \(y = \log_{\frac{1}{12}} x\)</mcq-option>
<mcq-option>(B) \(y = \log_{12} \frac{1}{x}\)</mcq-option>
<mcq-option>(C) \(y = \log_{x} 12\)</mcq-correct>
<mcq-correct>(D) \(y = \log_{12} x\)</mcq-correct>
</answer>

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"question_type": "Multiple Choice",
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"Algebra",
"Exponential Inverse"
]
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