Question

If Logk^a/y-z=Logk^b/z-x=Logk^c/x-y, what is the value of abc?​

Answer 1

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.