what is the approximate value of $q$ in the equation below?

$q + \log_{2}6 = 2q + 2$

-1.613
-1.522
0.585
3.079

Question

what is the approximate value of $q$ in the equation below?

$q + \log_{2}6 = 2q + 2$

-1.613
-1.522
0.585
3.079

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Logarithmic Equations", "Change of Base Formula" ], "new_concepts": [], "current_concepts": [ "Logarithmic Equations", "Change of Base Formula" ] } ## Isolate the variable q $$ \begin{aligned} q + \log_{2}6 &= 2q + 2 \ \log_{2}6 - 2 &= 2q - q \ q &= \log_{2}6 - 2 \end{aligned} $$ ## Evaluate the logarithm $$ \begin{aligned} \log_{2}6 &= \frac{\ln 6}{\ln 2} \approx 2.58496 \ q &\approx 2.58496 - 2 \ q &\approx 0.585 \end{aligned} $$

-1.613

-1.522

0.585

3.079

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

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QUESTION IMAGE

Question

Explanation:

Isolate the variable q

Evaluate the logarithm

Answer: