wiz-icon
MyQuestionIcon
MyQuestionIcon
4
You visited us 4 times! Enjoying our articles? Unlock Full Access!
Question

The value of the determinant ∣∣ ∣ ∣∣loga(x/y)loga(y/z)loga(z/x)logb(y/z)logb(z/x)logb(x/y)logc(z/x)logc(x/y)logc(y/z)∣∣ ∣ ∣∣ is

A
1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
-1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
logaxyz
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
none of these
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is D none of these
∣ ∣ ∣loga(x/y)loga(y/z)loga(z/x)logb(y/z)logb(z/x)logb(x/y)logc(z/x)logc(x/y)logc(y/z)∣ ∣ ∣
=∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣loge(x/y)logealoge(y/z)logealoge(z/x)logealoge(y/z)logebloge(z/x)logebloge(z/x)logebloge(x/y)logecloge(x/y)logecloge(y/z)logec∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣
=1logealogeblogec∣ ∣ ∣loge(x/y)loge(y/z)loge(z/x)loge(y/z)loge(z/x)loge(x/y)loge(z/x)loge(x/y)loge(y/z)∣ ∣ ∣
=1logealogeblogec∣ ∣logexlogeylogeylogezlogezlogexlogeylogezlogezlogexlogexlogeylogezlogexlogexlogeylogeylogez∣ ∣
C1C1+C2+C3
=1logealogeblogec∣ ∣0logeylogezlogezlogex0logezlogexlogexlogey0logexlogeylogeylogez∣ ∣
=0

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Fruendlich and Langmuir Isotherms
CHEMISTRY
Watch in App
Join BYJU'S Learning Program
CrossIcon