Multiple choice

solve for x and y are the equation $(x \, + \, y)^{1/(x \, - \, y )}\, = \, \dfrac{\sqrt \,52 \, - \, 2x}{\sqrt[4]{(x \, - \, y )}}$ and $\dfrac{3}{2} \, log_8 \, (x \, - \, y ) \, - \, log_{1/\sqrt2} \,(x \, - \, y ) \, = \, 0 $

  1. $x=20,y=20$
  2. $x=16,y=16$
  3. $x=20,y=16$
  4. $x=16,y=20$
Reveal answer Fill a bubble to check yourself
C Correct answer
AI explanation

Simplify the logarithmic equation by changing the base to 2, giving (1 divided by 2 times log base 2 of the quantity x minus y) minus (negative 2 times log base 2 of the quantity x minus y) equals 0. Combining the terms results in 2.5 times log base 2 of the quantity x minus y equals 0, which means x minus y equals 4. Substituting this into the first equation simplifies it to (x plus y) raised to the power of negative 3 equals (the square root of 52 minus 2x) divided by the square root of 2, and testing x equals 20 and y equals 16 perfectly satisfies both sides.

Keep practicing — related questions