ACT Math Practice Question #1204 (Medium (29)) | Test Citadel
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ACT Math Difficulty: Medium (29)

Digital ACT Math Practice Question #1204

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

If $\log_2(x) + \log_2(x - 6) = 4$, what is the real solution for $x$?
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Socratic AI Engine Step-by-Step Derivation
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⚡ 15-Second Desmos Speed Hack

Back-test the answer choices directly! Plug in $x = 8$: $\log_2(8) + \log_2(2) = 3 + 1 = 4$. It checks out immediately without solving the quadratic.

Masterclass Solution & Distractor Trap Analysis

Use the log product rule: $\log_2(x(x - 6)) = 4$. Convert to exponential form: $x(x - 6) = 2^4 = 16$. This gives the quadratic equation $x^2 - 6x - 16 = 0$. Factoring yields $(x - 8)(x + 2) = 0$, giving candidate solutions $x = 8$ and $x = ...

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

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