Question

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

Answer 1

Here,

a, b, c are in G.P>

$b^2=ac$ .........(i)

Now taking log or both the sides

$\Rightarrow log(b{)}^2=logac$

$\Rightarrow 2logb=loga+logc$

$\Rightarrow logb-loga=logc-logb$

Thus, log a, log b, log c are in A.P.