If a, b, and c are in geometric progression then loga n, logb n and logc n are in
Answers
Answered by
26
they are in H.P.
a, b and c are in GP ( b^2=ac)
b^2=ac
logb^2= log a + log c
{all log are To base n }
loga , log b and logc are in AP
so, 1/loga , 1/logb and 1/logc are in HP
applying base changing law of log
loga to base n = 1/ {logn to base a}
==> 1/ loga = log(base a ) n
similarly , 1/log( base b ) n
and 1/log (base c) n
then
(loga n , logb n ,logc n) are in H.P.
a, b and c are in GP ( b^2=ac)
b^2=ac
logb^2= log a + log c
{all log are To base n }
loga , log b and logc are in AP
so, 1/loga , 1/logb and 1/logc are in HP
applying base changing law of log
loga to base n = 1/ {logn to base a}
==> 1/ loga = log(base a ) n
similarly , 1/log( base b ) n
and 1/log (base c) n
then
(loga n , logb n ,logc n) are in H.P.
Similar questions