solve $\log_3(x + 1) =
\log_6(5 - x)$ by graphing.

what equations should be graphed?

$y_1 = \frac{\log(x + 1)}{\log 3}$

$y_1 = \frac{\log 3}{\log(x + 1)}$

$y_2 = \frac{\log 6}{\log(5 - x)}$

$y_2 = \frac{\log(5 - x)}{\log 6}$

Question

solve $\log_3(x + 1) =
\log_6(5 - x)$ by graphing.

what equations should be graphed?

$y_1 = \frac{\log(x + 1)}{\log 3}$

$y_1 = \frac{\log 3}{\log(x + 1)}$

$y_2 = \frac{\log 6}{\log(5 - x)}$

$y_2 = \frac{\log(5 - x)}{\log 6}$

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 Exponential Equations Graphically" ], "new_concepts": [], "current_concepts": [ "Change of Base Formula", "Solving Exponential Equations Graphically" ] } ## Set up the system of equations To solve the equation $\log_3(x + 1) = \log_6(5 - x)$ by graphing, we define two separate functions representing each side of the equation: $$ y_1 = \log_3(x + 1) $$ $$ y_2 = \log_6(5 - x) $$ ## Apply change of base formula Using the *Change of Base Formula* knowledge point $$ \begin{aligned} &y_1 = \frac{\log(x + 1)}{\log 3}\ &y_2 = \frac{\log(5 - x)}{\log 6} \end{aligned} $$ ## Identify the correct options Using the *Solving Exponential Equations Graphically* knowledge point $$ \begin{aligned} &\text{First correct equation: } y_1 = \frac{\log(x + 1)}{\log 3}\ &\text{Second correct equation: } y_2 = \frac{\log(5 - x)}{\log 6} \end{aligned} $$

[x] $y_1 = \frac{\log(x + 1)}{\log 3}$

[ ] $y_1 = \frac{\log 3}{\log(x + 1)}$

[ ] $y_2 = \frac{\log 6}{\log(5 - x)}$

[x] $y_2 = \frac{\log(5 - x)}{\log 6}$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Change of Base Formula" ] }

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QUESTION IMAGE

Question

Explanation:

Set up the system of equations

Apply change of base formula

Identify the correct options

Answer: