Question 4.

We have, $(5.55)^x = (0.555)^y = 1000$

Taking log in base 10 on both sides,

x($\log_{10}555$-2) = y($\log_{10}555$-3) = 3

Then, x($\log_{10}555$-2) = 3.....(1)

y($\log_{10}555$-3) = 3 .....(2)

From (1) and (2)

=> $\log_{10}555$=$\ \frac{\ 3}{x}$+2=$\ \frac{\ 3}{y}+3$

=> $\frac{1}{x} - \frac{1}{y}$ = $\frac{1}{3}$