Question

If a, b, c are in G.P., then prove that $\log a^n,\log b^n,\log c^n$ are in A.P.

Answer 1

It is given that a, b, c are in G.P.

Therefore, $b^2=ac$

$(b^2{)}^n=(ac{)}^n$

$b^{2n}=a^n{c}^n$

$\log b^{2n}=\log a^n+\log c^n$

$2\log b^n=\log a^n+\log c^n$

$⟹\log a^n,\log b^n,\log c^n$ are in A.P.