Home » If (log_{2} y = 3 – log_{2} x^{frac{3}{2}}), find y when x = 4.

If (log_{2} y = 3 – log_{2} x^{frac{3}{2}}), find y when x = 4.

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
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)