Match the following : Column -I Column-II A. If x > 1 ,   y > 1 ,   z > 1 are in G.P., then log ex ⁡ e ,     log ey ⁡ e , log ez ⁡ e are in P. A.P. B. If a,b,c are three consecutive terms of a progression such that a - b b - c = a c then a, b, c are in Q. G.P. C. If a, b, c are in A.P. then 2 a x + 1 ,   2 b x + 1 ,   2 c x + 1   ( x ≠ 0 ) are in

Step-by-step solution

A. we have log ex ⁡ e ,    log ey ⁡ e ,   log ez ⁡ e ⇒ 1 1 + lnx ,   1 1 + lny ,   1 1 + lnz as x ,   y ,   z are in GP ⇒ ln x ,   ln y ,   ln z are in AP ⇒ 1 + ln x , 1 +   ln y , 1 +   ln z are in AP ⇒ 1 1 + lnx ,   1 1 + lny ,   1 1 + lnz are in HP B. a - b b - c = a c ⇒ b = 2 ac a + c ⇒ a ,   b ,   c   a r e   i n   H . P . C. Since a ,   b ,   c are in AP b -