what is the solution to the equation below?

$\log 7 + \log(x - 4) = 1$

$x = -\frac{38}{7}$

$x = -\frac{18}{7}$

$x = \frac{18}{7}$

$x = \frac{38}{7}$

Question

what is the solution to the equation below?

$\log 7 + \log(x - 4) = 1$

$x = -\frac{38}{7}$

$x = -\frac{18}{7}$

$x = \frac{18}{7}$

$x = \frac{38}{7}$

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 Product Rule", "Solving Logarithmic Equations" ], "new_concepts": [], "current_concepts": [ "Logarithmic Product Rule", "Solving Logarithmic Equations" ] } ## Apply the product rule of logarithms Using the *Logarithmic Product Rule* knowledge point $$ \begin{aligned} &\log 7 + \log(x-4) = 1 \ &\log(7(x-4)) = 1 \ &\log(7x - 28) = 1 \end{aligned} $$ ## Convert to exponential form Using the *Solving Logarithmic Equations* knowledge point $$ \begin{aligned} &10^1 = 7x - 28 \ &10 = 7x - 28 \end{aligned} $$ ## Solve for x Using the *Linear Equations* knowledge point $$ \begin{aligned} &7x = 38 \ &x = \frac{38}{7} \end{aligned} $$ ## Verify the solution Using the *Solving Logarithmic Equations* knowledge point $$ \begin{aligned} &x - 4 = \frac{38}{7} - 4 = \frac{10}{7} > 0 \end{aligned} $$

(A) $x = -\frac{38}{7}$

(B) $x = -\frac{18}{7}$

(C) $x = \frac{18}{7}$

(D) $x = \frac{38}{7}$

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

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QUESTION IMAGE

Question

Explanation:

Apply the product rule of logarithms

Convert to exponential form

Solve for x

Verify the solution

Answer: