If the positive numbers x,y,z are in harmonic progression, then log(x+z) + log(x-2y+z) equals a) 4log(x-z) b) 3log(x-z) c) 2log(x-z) d) log(x-z) How do i approach this problem? IF x,y,z are in HP, => y=2xy/x+z

Wyatt Weeks 2022-10-23 Answered
If the positive numbers x,y,z are in harmonic progression, then log ( x + z ) + log ( x 2 y + z ) equals
a ) 4 log ( x z ) b ) 3 log ( x z ) c ) 2 log ( x z ) d ) log ( x z )
How do i approach this problem? IF x,y,z are in HP, y = 2 x y / x + z
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Answers (1)

Remington Wells
Answered 2022-10-24 Author has 13 answers
We need to eliminate y
x + z 2 y = x + z 4 z x / ( z + x ) = ( z x ) 2 z + x
log ( z + x ) + log ( x + z 2 y ) = log ( z + x ) ( x + z 2 y )
= log ( z + x ) ( z x ) 2 z + x = log ( z x ) 2
If x > z , log ( z x ) 2 = 2 log ( x z )
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