If \(\log_{2} y = 3 – \log_{2} x^{\frac{3}{2}}\), find y when x = 4.
- 8
- \(\sqrt{65}\)
- 4\(\sqrt{2}\)
- 3
-
1
The correct answer is: E
Explanation
\(\log_{2} y = 3 - \log_{2} x^{\frac{3}{2}}\)
When x = 4,
\(\log_{2} y = 3 - \log_{2} 4^{\frac{3}{2}}\)
\(\log_{2} y = 3 - \log_{2} 2^{3}\)
\(\log_{2} y = 3 - 3 \log_{2} 2 = 3 - 3 = 0\)
\(\log_{2} y = 0 \implies y = 2^{0} = 1\)