which is the logarithmic form of $25 = 5^2$?
$\log_{2} 5 = 25$
$\log_{25} 2 = 5$
$\log_{5} 25 = 2$
$\log_{5} 2 = 25$

what is $\log_{3} 9 = x$ in exponential form?
$3^x = 9$
$9^x = 3$
$x^3 = 9$
$3^9 = x$

Question

which is the logarithmic form of $25 = 5^2$?
$\log_{2} 5 = 25$
$\log_{25} 2 = 5$
$\log_{5} 25 = 2$
$\log_{5} 2 = 25$

what is $\log_{3} 9 = x$ in exponential form?
$3^x = 9$
$9^x = 3$
$x^3 = 9$
$3^9 = x$

Accepted Answer

{ "quality": "clear", "question_count": 2, "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" ] } ## Convert exponential equation to logarithmic form Using the *Logarithmic and Exponential Inverses* knowledge point $$ \begin{aligned} &b^y = x \iff \log_b(x) = y\ &25 = 5^2 \implies \log_5(25) = 2 \end{aligned} $$ ## Convert logarithmic equation to exponential form Using the *Logarithmic and Exponential Inverses* knowledge point $$ \begin{aligned} &\log_b(x) = y \iff b^y = x\ &\log_3(9) = x \implies 3^x = 9 \end{aligned} $$ ## Question 1 (A) $\log_{2}5 = 25$

(B) $\log_{25}2 = 5$

(C) $\log_{5}25 = 2$

(D) $\log_{5}2 = 25$ ## Question 2 (A) $3^x = 9$

(B) $9^x = 3$

(C) $x^3 = 9$

(D) $3^9 = x$

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

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