27. If a, b, care the p th, q th, r th terms of a G.P., then find the value of
(q-rlog a + (r-p)log b + (p-q)logo
Answers
Answered by
0
Answer:
MATHS
If a, b, c are pth, qth and rth terms of a GP, then
∣
∣
∣
∣
∣
∣
∣
∣
loga
logb
logc
p
q
r
1
1
1
∣
∣
∣
∣
∣
∣
∣
∣
is equal to?
Share
Study later
ANSWER
Let d be common ratio of G.P & first terms be x.
a=xd
p−1
b=xd
q−1
c=xd
r−1
So
∣
∣
∣
∣
∣
∣
∣
∣
loga
logb
logc
p
q
r
1
1
1
∣
∣
∣
∣
∣
∣
∣
∣
⇒
∣
∣
∣
∣
∣
∣
∣
∣
logx+(p−1)logd
logx+(q−1)logd
logx+(r−1)logd
p
q
r
1
1
1
∣
∣
∣
∣
∣
∣
∣
∣
r
1
→r
1
−r
2
r
2
→r
2
−R
3
⇒
∣
∣
∣
∣
∣
∣
∣
∣
(p−a)logd
(q−r)logd
logx+(r−1)logd
p−q
q−r
r
0
0
1
∣
∣
∣
∣
∣
∣
∣
∣
(p−q)(q−r)
∣
∣
∣
∣
∣
∣
∣
∣
logd
logd
logx+(r−1)logd
1
1
r
0
0
1
∣
∣
∣
∣
∣
∣
∣
∣
=0
∵ two rows are same.
solution
Similar questions