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If x, y, z are in HP, then log (x + z) + log (x- 2y + z) is equal to

Option: 1

log (x-z)


Option: 2

2 log (x-z)


Option: 3

3 log (x-z)


Option: 4

4 log (x-z)


Answers (1)

best_answer

As we learn

General term of HP

T_{n}= \frac{1}{a+\left ( n-1 \right )d}

where

here a= \frac{1}{a_{1}} and d= \frac{1}{a_{2}}-\frac{1}{a_{1}}

 

 

y = \frac{2xz}{x+z}

log (x + z) + log (x- 2y + z) 

=  log (x + z) . (x- 2y + z)

= log [(x + z)2- 2y (x + z)] 

=  log ((x+z)^{2}-2y\frac{2xz}{y})

= log [(x + z)2- 4xz] = log (x-z)2 = 2log (x-z)

 

 

Posted by

Rishi

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