Question

if a,b,c are in G.P . prove that log a,log b,and log c are in A.P

Answer 1

HEY BUDDY...!!!

HERE'S THE ANSWER...

_______________________

▶️ Given a , b , c are in G.P , So

✔️ [ b / a = c / b ] // Common ratio ______ ( 1 )


♠️ Now multiplying log both sides in eqn ( 1 )

=> b / a = c / b

=> log ( b / a ) = log ( c / b )_______( 2 )

▶️ Using property of log

♠️ [ log ( x / y ) = log x - log y ]

✔️ Now by using this property eqn ( 2 ) becomes

=> { log b - log a = log c - log b }

⏺️ We can conclude this as Common difference in AP , i.e

✔️ log a , log b , log c are in A.P.


♠️ HENCE PROVED ✔️✔️




HOPE HELPED !!



JAI HIND !!!


:-)