consider $8^{x-4} = 8^{10}$

because the bases are equal, the exponents must also be equal.

the solution to the equation is $x =$

Question

consider $8^{x-4} = 8^{10}$

because the bases are equal, the exponents must also be equal.

the solution to the equation is $x =$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Solving Exponential Equations Algebraically" ], "new_concepts": [], "current_concepts": [ "Solving Exponential Equations Algebraically" ] } ## Equate the exponents Using the *Solving Exponential Equations Algebraically* knowledge point $$ \begin{aligned} &8^{x-4} = 8^{10} \ &x - 4 = 10 \end{aligned} $$ ## Solve for x Using the *Solving Exponential Equations Algebraically* knowledge point $$ \begin{aligned} &x = 10 + 4 \ &x = 14 \end{aligned} $$ The solution to the equation is $x =$ 14. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Solving Exponential Equations Algebraically" ] }

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QUESTION IMAGE

Question

Explanation:

Equate the exponents

Solve for x

Answer: