SOLUTION: Given the relation: log(a)/y-z=log(b)/z-x=log(c)/x-y Prove a^x·b^y·c^z=1

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Given the relation: log(a)/y-z=log(b)/z-x=log(c)/x-y Prove a^x·b^y·c^z=1       Log On


   

Question 975839: Given the relation: log(a)/y-z=log(b)/z-x=log(c)/x-y
Prove a^x·b^y·c^z=1
Answer by amarjeeth123(570) About Me  (Show Source):
You can put this solution on YOUR website!
Let log(a)/y-z=log(b)/z-x=log(c)/x-y=k
log(a)=k(y-z)
a=10^k(y-z)
log(b)=k(z-x)
b=10^k(z-x)
log(c)=k(x-y)
c=10^k(x-y)
a^x.b^y.c^z=10^[k.x.(y-z)].10^[ky(z-x)].10^[kz(x-y)]
=10^[k{x(y-z)+y(z-x)+z(x-y)}]
=10^(0)
=1.