If \(\log_{2} y = 3 - \log_{2} x^{\frac{3}{2}}\), find y when x = 4.
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Correct Answer: Option E
Explanation:
\(\log_{2} y = 3 - \log_{2} x^{\frac{3}{2}}\)
When x = 4,
\(\log_{2} y = 3 - \log_{2} 4^{\frac{3}{2}}\)
\(\log_{2} y = 3 - \log_{2} 2^{3}\)
\(\log_{2} y = 3 - 3 \log_{2} 2 = 3 - 3 = 0\)
\(\log_{2} y = 0 \implies y = 2^{0} = 1\)
\(\log_{2} y = 3 - \log_{2} x^{\frac{3}{2}}\)
When x = 4,
\(\log_{2} y = 3 - \log_{2} 4^{\frac{3}{2}}\)
\(\log_{2} y = 3 - \log_{2} 2^{3}\)
\(\log_{2} y = 3 - 3 \log_{2} 2 = 3 - 3 = 0\)
\(\log_{2} y = 0 \implies y = 2^{0} = 1\)