If x- y- z are in H-P- then the value of expression log x-z-log x-2 y-z will beA- log x - z B- 2 log x-zC- 3 log x - z D- 4 log x - z

The correct option is B 2log(x z)If x,y,z are in H.P., then y =2xz/x+z Now, log_e(x+z)+log_e(x 2y+z) =log_e{ (x+z)(x 2y+z) } =log_e [ (x+z)(x+z 4xz/x+z ) ] ...

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Question

If x, y, z are in H.P., then the value of expression log(x + z) + log(x - 2y + z) will be

log(x-z)

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2log(x-z)

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3log(x-z)

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4log(x-z)

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Solution

The correct option is B 2log(x-z)
If x,y,z are in H.P., then y = $\frac{2 x z}{x + z}$
Now, $l o g_{e} (x + z) + l o g_{e} (x - 2 y + z)$
$= l o g_{e} {(x + z) (x - 2 y + z)} = l o g_{e} [(x + z) (x + z - \frac{4 x z}{x + z})] = l o g_{e} [(x + z)^{2} - 4 x z] = l o g_{e} (x - z)^{2} = 2 l o g_{e} (x - z)$

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If x, y, z are in H.P., then the value of expression log(x + z) + log(x - 2y + z) will be

The correct option is B 2log(x-z)If x,y,z are in H.P., then y =2xzx+z Now, loge(x+z)+loge(x−2y+z) =loge{(x+z)(x−2y+z)}=loge[(x+z)(x+z−4xzx+z)]=loge[(x+z)2−4xz]=loge(x−z)2=2loge(x−z)