If $$5^x=30^-y = 6^z$$, then what is the value of $$\frac{(xy + yz + zx)}{xyz}$$ ?
Let $$5^x=30^-y = 6^z=k$$
=> $$5=k^{\frac{1}{}}$$ , $$30=k^{\frac{-1}{y}}$$ and $$6=k^{\frac{1}{z}}$$
Also, $$30=5\times6$$
=> $$k^{\frac{-1}{y}}=k^{\frac{1}{x}}\times k^{\frac{1}{z}}$$
=>Â $$k^{\frac{-1}{y}}=k^{\frac{1}{x}+\frac{1}{z}}$$
=> $$\frac{-1}{y}=\frac{1}{x}+\frac{1}{z}$$
=> $$\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=0$$
=> $$\frac{yz+zx+xy}{xyz}=0$$
=> Ans - (A)
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