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

Question:

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

Solution:

a ,b and c are in G.P.

$\therefore b^{2}=a c$

Now, taking $\log$ on both the sides:

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

$\Rightarrow 2 \log b=\log a+\log c$

Thus, $\log a, \log b$ and $\log c$ are in A.P.