Value of Reciprocal Difference in Exponents

$(5.55)^x = 10^3 \implies 5.55 = 10^{3/x}$. Also, $(0.555)^y = 10^3 \implies 0.555 = 10^{3/y}$. Dividing the two expressions: $\frac{5.55}{0.555} = \frac{10^{3/x}}{10^{3/y}} \implies 10 = 10^{3(1/x - 1/y)}$. Thus, $3\left(\frac{1}{x} - \frac{1}{y}\right) = 1 \implies \frac{1}{x} - \frac{1}{y} = \frac{1}{3}$.