solve logarithmic equation

$\log_{2}(x+24) = 6$

rewrite without logarithms

solve equation

Question

solve logarithmic equation

$\log_{2}(x+24) = 6$

rewrite without logarithms

solve equation

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Logarithmic Evaluation" ], "new_concepts": [ "Logarithmic Equations" ], "current_concepts": [ "Logarithmic Evaluation", "Logarithmic Equations" ] } ## Convert to exponential form Using the *Logarithmic Evaluation* knowledge point $$ \begin{aligned} &\log_{2}(x+24) = 6 \ &x + 24 = 2^6 \end{aligned} $$ ## Evaluate the power of two Using the *Logarithmic Evaluation* knowledge point $$ \begin{aligned} &2^6 = 64 \ &x + 24 = 64 \end{aligned} $$ ## Solve the linear equation Using the *Logarithmic Evaluation* knowledge point $$ \begin{aligned} &x = 64 - 24 \ &x = 40 \end{aligned} $$ $$x = 40$$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Logarithmic Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Convert to exponential form

Evaluate the power of two

Solve the linear equation

Answer: