If three distinct positive reals x,y,z are in H.P. and `x gt z`, then show that
`log(x+z)+log(x-2y+z)=2log(x-z)`

If x,y,z are in HP, then show that log(x+z)+log(x+z-2y)=2 log (x-z)

If ln(x+z)+ln(x-2y+z)=2ln(x-z) then

(i) The value of x + y + z is 15. If a, x, y, z, b are in AP while the value of (1)/(x) + (1)/(y) + (1)/(z) " is " (5)/(3) . If a, x, y, z b are in HP, then find a and b (ii) If x,y,z are in HP, then show that log (x +z) + log (x +z -2y) = 2 log ( x -z) .

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

If x,y,z are in G.P. then log x , log y, logz, are in

If x,y,z are in G.P. (x,y,z gt 1) , then (1)/(2x+log_(e)x) , (1)/(4x+log_(e)y) , (1)/(6x+log_(ez)z) are in