prove that (a^x/a^y)^z × (a^y/a^z)^x × (a^z/a^x)^y = 1
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1
Answer:
Explanation:
Let us take
log
a
of the first to get:
log
a
y
=
1
1
−
log
a
x
And also of the second:
log
a
z
=
1
1
−
log
a
y
Substitute the first into the second:
log
a
z
=
1
1
−
1
1
−
log
a
x
Rearrange:
log
a
z
=
1
1
−
log
a
x
−
1
1
−
log
a
x
change sign on the right and rearrange again:
log
a
z
log
a
x
=
log
a
x
−
1
log
a
z
log
a
x
−
log
a
x
=
−
1
Collect
log
a
x
:
log
a
x
[
log
a
z
−
1
]
=
−
1
Change sign and isolate
log
a
x
:
log
a
x
=
1
1
−
log
a
z
Take the power of
a
on both sides:
x
=
a
1
1
−
log
a
z
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