use desmos or a graphing calculator to solve the equation
$3^{x-1} = 11$.

$x \approx \underline{\quad\quad\quad}$

Question

use desmos or a graphing calculator to solve the equation
$3^{x-1} = 11$.

$x \approx \underline{\quad\quad\quad}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Exponential Functions" ], "new_concepts": [ "Logarithmic Equations", "Solving Exponential Equations" ], "current_concepts": [ "Exponential Functions", "Logarithmic Equations", "Solving Exponential Equations" ] } ## Apply logarithms to both sides $$ \ln(3^{x-1}) = \ln(11) $$ ## Solve for x $$ \begin{aligned} (x-1)\ln(3) &= \ln(11) \ x-1 &= \frac{\ln(11)}{\ln(3)} \ x &= 1 + \frac{\ln(11)}{\ln(3)} \end{aligned} $$ ## Calculate the decimal approximation $$ \begin{aligned} x &\approx 1 + \frac{2.397895}{1.098612} \ x &\approx 1 + 2.182658 \ x &\approx 3.18 \end{aligned} $$ Use Desmos or a Graphing Calculator to solve the equation $3^{x-1} = 11$. $x \approx$ 3.18 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Solving Exponential Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Apply logarithms to both sides

Solve for x

Calculate the decimal approximation

Answer: