plz friends don't answer Irrelevant....
Answers
Answer:
Using property:- p=\log_qr\implies q^{p}=rp=log
q
r⟹q
p
=r
\begin{gathered}x=\log_abc\implies a^{x}=bc\\\;\\y=\log_bca\implies b^{x}=ca\\\;\\z=\log_cab\implies c^{x}=ab\end{gathered}
x=log
a
bc⟹a
x
=bc
y=log
b
ca⟹b
x
=ca
z=log
c
ab⟹c
x
=ab
Now,
\begin{gathered}a^{xyz}=(a^{x})^{yz}\\\;\\=(bc)^{yz}\\\;\\=(b^{y})^{z}\times(c^{z})^{y}\\\;\\=(ca)^{z}\times(ab)^{y}\\\;\\=c^{z}.a^{z}\times a^{y}.b^{y}\\\;\\=ab.a^{z+y}.b^{y}\\\;\\=a^{1+z+y}\times b.b^{y}\\\;\\=a^{1+z+y}\times b.ca\\\;\\=a^{1+z+y+1}\times bc\\\;\\=a^{2+z+y}.a^{x}\\\;\\a^{xyz}=a^{x+y+z+2}\\\;\\xyz=x+y+z+2\\\;\\xyz-x-y-z=2\end{gathered}
a
xyz
=(a
x
)
yz
=(bc)
yz
=(b
y
)
z
×(c
z
)
y
=(ca)
z
×(ab)
y
=c
z
.a
z
×a
y
.b
y
=ab.a
z+y
.b
y
=a
1+z+y
×b.b
y
=a
1+z+y
×b.ca
=a
1+z+y+1
×bc
=a
2+z+y
.a
x
a
xyz
=a
x+y+z+2
xyz=x+y+z+2
xyz−x−y−z=2