1/(logxy x * y * z) + 1/(logyz x * y * z) + 1/(logxx x * y * z) =
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Step-by-step explanation:
We are given,
D=
∣
∣
∣
∣
∣
∣
∣
∣
1
log
y
x
log
z
x
log
x
y
1
log
z
y
log
x
z
log
y
z
1
∣
∣
∣
∣
∣
∣
∣
∣
[Now, from the logarithmic properties, log
a
b=
log
c
a
log
c
b
]
D=
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
1
log
e
y
log
e
x
log
e
z
log
e
x
log
x
log
e
y
1
log
e
z
log
e
y
log
e
x
log
e
z
log
e
y
log
e
z
1
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
D=
log
e
xlog
e
ylog
e
z
1
∣
∣
∣
∣
∣
∣
∣
∣
log
e
x
log
e
x
log
e
x
log
e
y
log
e
y
log
e
y
log
e
z
log
e
z
log
e
z
∣
∣
∣
∣
∣
∣
∣
∣
(taking common from each raw)
D=
log
e
xlog
e
ylog
e
z
1
(0)
(from the rules of determinant that
∣
∣
∣
∣
∣
∣
∣
∣
a
a
x
b
b
y
c
c
z
∣
∣
∣
∣
∣
∣
∣
∣
=0)
D=0.
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