what is the inverse of the logarithmic function $f(x) = \log_{9}x$?

$f^{-1}(x) = x^{9}$
$f^{-1}(x) = -\log_{9}x$
$f^{-1}(x) = 9^{x}$
$f^{-1}(x) = \frac{1}{\log_{9}x}$

Question

what is the inverse of the logarithmic function $f(x) = \log_{9}x$?

$f^{-1}(x) = x^{9}$
$f^{-1}(x) = -\log_{9}x$
$f^{-1}(x) = 9^{x}$
$f^{-1}(x) = \frac{1}{\log_{9}x}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Logarithmic and Exponential Inverses" ], "new_concepts": [], "current_concepts": [ "Logarithmic and Exponential Inverses", "Logarithmic Functions" ] } ## Set up the inverse equation Using the *Logarithmic and Exponential Inverses* knowledge point $$ \begin{aligned} &y = \log_{9}x \ &x = \log_{9}y \end{aligned} $$ ## Solve for y Using the *Logarithmic and Exponential Inverses* knowledge point $$ y = 9^x $$ ## Write the final inverse function Using the *Logarithmic and Exponential Inverses* knowledge point $$ f^{-1}(x) = 9^x $$

$f^{-1}(x) = x^9$

$f^{-1}(x) = 9^x$

$f^{-1}(x) = -\log_{9}x$

$f^{-1}(x) = \frac{1}{\log_{9}x}$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Logarithmic and Exponential Inverses" ] }

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Set up the inverse equation

Solve for y

Write the final inverse function

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