ACT Math Practice Question #1403 (Hard (33)) | Test Citadel
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ACT Math Difficulty: Hard (33)

Digital ACT Math Practice Question #1403

Test your problem-solving accuracy on this official-caliber item. Select an answer choice to check your reasoning instantly.

If log_3(x - 2) + log_3(x + 6) = 2, what is the value of x?
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Socratic AI Engine Step-by-Step Derivation
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Plug in x = 3: log_3(1) + log_3(9) = 0 + 2 = 2. Instant match!

Masterclass Solution & Distractor Trap Analysis

Log_3((x - 2)(x + 6)) = 2 -> (x - 2)(x + 6) = 3^2 = 9. x^2 + 4x - 21 = 0 -> (x + 7)(x - 3) = 0. Since x > 2, x = 3....

Distractor Analysis: Trap choice eliminates careless test-takers who confuse roots with coordinates...

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