SAT Math Practice Question #468 (Hard (800)) | Test Citadel
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SAT Math Difficulty: Hard (800)

Digital SAT Math Practice Question #468

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

The solution to the equation \[ 2^{x+2} \cdot 3^{x-1} = 5^{2x} \] is \( x \). Which of the following expressions is equivalent to \( x \)?
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Socratic AI Engine Step-by-Step Derivation
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Tactical Insight (Hint 1)

A system of equations represents geometric intersections. Consider substitution, elimination, or setting both expressions equal.

Elimination Framework (Hint 2)

Desmos Tactical Shortcut: Plot the left-hand side and right-hand side as separate equations (e.g. \( y_1 = f(x) \) and \( y_2 = g(x) \)). Click the intersection points directly to read exact coordinates.

Masterclass Solution & Distractor Trap Analysis

This problem tests your advanced exponent rules and logarithm manipulation. If you're going for an 800, you must be comfortable pulling apart exponents. **Step 1: Deconstruct the exponents** Whenever you see addition or subtraction in an ex...

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

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