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-zB- 2 log x-zC- 3 log x-zD- 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+ ...

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Byju's Answer

Standard XII

Mathematics

nth Term of HP

If x , y , z ...

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)