SOLUTION: Show that log[base 2]9 x log[base 3]8 = log[base 2]8 x log[base 3]9. Thank you.

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Show that log[base 2]9 x log[base 3]8 = log[base 2]8 x log[base 3]9. Thank you.      Log On


   

Question 30061: Show that
log[base 2]9 x log[base 3]8 = log[base 2]8 x log[base 3]9.
Thank you.
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
log[base 2]9 x log[base 3]8 = log[base 2]8 x log[base 3]9.
USING THE FORMULA
LOG (A) TO BASE B =LOG(A)/LOG(B)....TO ANY COMMON BASE WE GET
log[base 2]9 x log[base 3]8 = log[base 2]8 x log[base 3]9.
LHS={LOG(9)/LOG(2)}*{LOG(8)/LOG(3)}=LOG(9)*LOG(8)/{LOG(2)*LOG(3)}
RHS={LOG(8)/LOG(2)}*{LOG(9)/LOG(3)}=LOG(9)*LOG(8)/{LOG(2)*LOG(3)}
=LHS