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Question

If log(x+z)+log(x2y+z)=2log(xz), then 
  1. y(x+z)=2xz
  2. z(z+y)=2xy
  3. x2z2=y
  4. x+z=3y


Solution

The correct option is A y(x+z)=2xz
log(x+z)+log(x2y+z)=2log(xz)log(x+z)(x2y+z)=2log(xz)log(x+z)(x2y+z)log(xz)=log(xz)log(x+z)(x2y+z)(xz)=log(xz)(x+z)(x2y+z)(xz)=(xz)(x+z)(x2y+z)=(xz)2(x+z)22y(x+z)=(xz)22xz2yx2yz=2xz2xz=xy+yz

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