Question

If a, b , c be in the G.P. then prove that $log{a}^n,log{b}^n,log{c}^n,$ are in A . P

Answer 1

Gives the a , b , c are G . P .
We have to prove that $log{a}^{n}log{b}^{n}log{c}^n$ to be A . P
or n log a , n log b , n log c to be in A . P
or 2log b = log a + log b
We have cancelled
or $log{b}^2=logacor{b}^2=ac$
Which is true by (1)