Let a and R be the first term and common ratio of a Gp respectively. So, Tp=aRp−1=x Tq=aRq−1=y and Tr=aRr−1=z ⇒ log x = log a + (p - 1) log R log y = log a + (q - 1) log R and log z = log a + (r - 1) log R ∴|
log‌x
p
1
log‌y
q
1
log‌z
r
1
|=|
log‌a+(p−1)‌logR
p
1
log‌a+(q−1)‌logR
q
1
log‌a+(r−1)‌logR
r
1
| =|
log‌a
p
1
log‌a
q
1
log‌a
r
1
|+|
(p−1)‌logR
p
1
(q−1)‌logR
q
1
(r−1)‌logR
r
1
| = log a |
1
p
1
1
q
1
1
r
1
|+logR|
p−1
p−1
1
q−1
q−1
1
r−1
r−1
1
|(C2→C2−C3) = 0 + 0 = 0 (∵ two columns are identical)