ACT Math Practice Question #1286 (Medium (32)) | Test Citadel
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ACT Math Difficulty: Medium (32)

Digital ACT Math Practice Question #1286

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

If $\log_{10}(x) = 2$ and $\log_{10}(y) = -3$, what is the value of $\log_{10}\left(\frac{100x^3}{\sqrt{y}}\right)$?
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Socratic AI Engine Step-by-Step Derivation
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Remember $\log(100) = 2$. Power rule: $2 + 3(2) - 0.5(-3) = 2 + 6 + 1.5 = 9.5$.

Masterclass Solution & Distractor Trap Analysis

Expand the expression using logarithm properties: $$\log_{10}\left(\frac{100x^3}{y^{1/2}}\right) = \log_{10}(100) + \log_{10}(x^3) - \log_{10}(y^{1/2})$$ $$= 2 + 3\log_{10}(x) - \frac{1}{2}\log_{10}(y).$$ Substitute $\log_{10}(x) = 2$ and $...

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

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