If x,y,z are in H.P. then the value of log(x+z)+log(x−2y+z)
A
2log|(x−z)|
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
2log|(y−z)|
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
4log|(x−z)|
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
log|(y−z)|
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is A2log|(x−z)| ∵x,y,zϵ A.P ⇒y=2xzx+z..(1) Now log(x+z)+log(x−2y+z)=log(x+z)+log(x+z−4xzx+z) using (1) =log(x+z)+log((x+z)2−4xz)−log(x+z)=log(x−z)2=2log|x−z| Hence, option 'A' is correct.