Discussion

Explanation:

Let 5^x = (0.125)^y = 10^3z = k

Hence, 5 = k^1/x

0.125 = k^1/y and 

10 = k^1/3z

We know that 0.125 = (0.5)³ = (5/10)³

Hence,  $k^{\frac{1}{y}} = {\left(\frac{k^{\frac{1}{x}}}{k^{\frac{1}{3z}}}\right)}^3=k^{\frac{3}{x}-\frac{1}{z}}$

⇒ $\frac{1}{y}=\frac{3}{x}-\frac{1}{z}$

⇒ $\frac{3}{x}=\frac{1}{y}+\frac{1}{z}$

Hence, option (b).

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