Question

if a, b, c are in GP. prove that logbase( a )x, log base(b) x, log base(c )x in HP. What I write in the bracket are bases​

Answer 1

Answer:

a, b, c are in GP

⇒b

2

=ac

Taking log base x on both sides:-

⇒log

x

(b

2

)=log

x

(ac)

⇒2log

x

b=log

x

a+log

x

c

∴log

x

a,log

x

b,log

x

c are in AP

⇒

log

x

a

1

,

log

x

b

1

,

log

x

c

1

are in HP

⇒log

a

x,log

b

x,log

c

x are in HP.