If (a)raised to pow x = b, (b)raised to pow y = c , (c)raised to pow z = a
prove that xyz = 1
2006-09-06 22:59:53 · 4 answers · asked by jojo 1 in Education & Reference ➔ Homework Help
We are given: a^x = b, b^y = c, c^z = a.
Since b = a^x, it follows that b^y = (a^x)^y.
Since b^y = c, it follows that (a^x)^y = c
Since c^z = a, it follows that ((a^x)^y)^z = a
By one of the rules of exponents, ((a^x)^y)^z = a^(xyz)
Hence, a^(xyz) = a
Therefore, xyz must equal 1.
2006-09-06 23:23:02 · answer #1 · answered by Bramblyspam 7 · 0⤊ 0⤋
what you have is:
(a)^x = b ----- eq 1
(b)^y = c ----- eq 2
(c)^z = a ----- eq 3
Using substitution (eq 3 into eq 1 into eq 2):
a = (c)^z -> (a)^x = b = ((c)^z)^x
((c)^z)^x = b -> (b)^y = c = (((c)^z)^x)^y
so since
((c^z)^x)^y = c
(c)^(z*x*y) = c^1
only true if x*y*z = 1
2006-09-06 23:07:34 · answer #2 · answered by Absent Glare 3 · 0⤊ 0⤋
1x1x1
2006-09-06 23:03:28 · answer #3 · answered by kaeleymel 3 · 0⤊ 0⤋
i really have no idea
2006-09-06 23:06:56 · answer #4 · answered by bay-from-indonesia 1 · 0⤊ 0⤋