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If $\log_{2} y = 3 - \log_{2} x^{\frac{3}{2}}$ , find y whe...

If $\log_{2} y = 3 - \log_{2} x^{\frac{3}{2}}$ , find y when x = 4.

A.

8

B.

$\sqrt{65}$

C.

4 $\sqrt{2}$

D.

3

E.

1

View answer & explanation

Correct answer is E

$\log_{2} y = 3 - \log_{2} x^{\frac{3}{2}}$

When x = 4,

$\log_{2} y = 3 - \log_{2} 4^{\frac{3}{2}}$

$\log_{2} y = 3 - \log_{2} 2^{3}$

$\log_{2} y = 3 - 3 \log_{2} 2 = 3 - 3 = 0$

$\log_{2} y = 0 \implies y = 2^{0} = 1$

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