solve $\log_{8}12 = x - 2$. round your answer to four decimal places.

$x \approx -0.8050$
$x \approx 3.1950$
$x \approx 2.8368$
$x \approx 3.5850$

Question

solve $\log_{8}12 = x - 2$. round your answer to four decimal places.

$x \approx -0.8050$
$x \approx 3.1950$
$x \approx 2.8368$
$x \approx 3.5850$

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": [ "Solving Logarithmic Equations", "Change of Base Formula" ], "new_concepts": [], "current_concepts": [ "Solving Logarithmic Equations", "Change of Base Formula" ] } ## Isolate the variable x Using the *Solving Logarithmic Equations* knowledge point $$ \begin{aligned} &\log_{8}12 = x - 2\ &x = \log_{8}12 + 2 \end{aligned} $$ ## Apply change of base formula Using the *Change of Base Formula* knowledge point $$ \begin{aligned} &\log_{8}12 = \frac{\ln 12}{\ln 8}\ &x = \frac{\ln 12}{\ln 8} + 2 \end{aligned} $$ ## Calculate the numerical value Using the *Change of Base Formula* knowledge point $$ \begin{aligned} &\ln 12 \approx 2.4849066\ &\ln 8 \approx 2.0794415\ &\log_{8}12 \approx \frac{2.4849066}{2.0794415} \approx 1.1949875\ &x \approx 1.1949875 + 2 = 3.1949875\ &x \approx 3.1950 \end{aligned} $$

(A) $x \approx -0.8050$

(B) $x \approx 3.1950$

(C) $x \approx 2.8368$

(D) $x \approx 3.5850$

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

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QUESTION IMAGE

Question

Explanation:

Isolate the variable x

Apply change of base formula

Calculate the numerical value

Answer: