if loga/y+z=logb/z+x=logc/x+y prove that (b/c)^x × (c/a)^y × (a/b)^z = 1
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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.
Step-by-step explanation:
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