Question 39

If $$5^x=30^-y = 6^z$$, then what is the value of $$\frac{(xy + yz + zx)}{xyz}$$ ?

Solution

Let $$5^x=30^-y = 6^z=k$$

=> $$5=k^{\frac{1}{}}$$ , $$30=k^{\frac{-1}{y}}$$ and $$6=k^{\frac{1}{z}}$$

Also, $$30=5\times6$$

=> $$k^{\frac{-1}{y}}=k^{\frac{1}{x}}\times k^{\frac{1}{z}}$$

=> $$k^{\frac{-1}{y}}=k^{\frac{1}{x}+\frac{1}{z}}$$

=> $$\frac{-1}{y}=\frac{1}{x}+\frac{1}{z}$$

=> $$\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=0$$

=> $$\frac{yz+zx+xy}{xyz}=0$$

=> Ans - (A)

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