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

$\log_{5} 15 = x + 3$

$\bigcirc$ $-2.523$
$\bigcirc$ $-1.317$
$\bigcirc$ $2.880$
$\bigcirc$ $7.485$

Question

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

$\log_{5} 15 = x + 3$

$\bigcirc$ $-2.523$
$\bigcirc$ $-1.317$
$\bigcirc$ $2.880$
$\bigcirc$ $7.485$

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": [ "Change of Base Formula", "Solving Logarithmic Equations" ], "new_concepts": [], "current_concepts": [ "Change of Base Formula", "Solving Logarithmic Equations" ] } ## Evaluate the logarithm Using the *Change of Base Formula* knowledge point $$ \log_{5}15 = \frac{\ln 15}{\ln 5} \approx \frac{2.70805}{1.60944} \approx 1.6826 $$ ## Solve for x Using the *Solving Logarithmic Equations* knowledge point $$ \begin{aligned} 1.6826 &\approx x + 3 \ x &\approx 1.6826 - 3 \ x &\approx -1.3174 \end{aligned} $$

(A) $-2.523$

(B) $-1.317$

(C) $2.880$

(D) $7.485$

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

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Question

Explanation:

Evaluate the logarithm

Solve for x

Answer: