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Question

If x,y,z are in H.P, then log|x+z|+log|x2y+z| is equal to

A
log|xz|
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B
2log|xz|
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C
2log|x+z|
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D
none of these
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Solution

The correct option is B 2log|xz|
Given, x,y,z are in H.P.
y=2xzx+z
(x+z)y=2xz ...(1)

log|x+z|+log|x2y+z|
=log(x+z)(x+z2y)
=log(x+z)22y(x+z)
=log(x+z)24xz [From (1)]
=log(xz)2 =2logxz

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