SOLUTION: if logarithm a + logarithm b + logarithm c +.......,is an arithmetic progression, show that a+b+c +.........is a geometric progression

Algebra ->  Sequences-and-series -> SOLUTION: if logarithm a + logarithm b + logarithm c +.......,is an arithmetic progression, show that a+b+c +.........is a geometric progression       Log On


   

Question 997978: if logarithm a + logarithm b + logarithm c +.......,is an arithmetic progression, show that a+b+c +.........is a geometric progression

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Since we are given that

log(a) + log(b) + log(c) + ... is an arithmetic progression,

then log(b)-log(a) = log(c)-log(b) = ... = the common difference

Therefore by a principle of logs, log(b/a) = log(c/d) = ... 

Therefore b/a = c/d = ... = common ratio of a,b,c,...

Therefor a,b,c,... is a geometric progression.

Edwin