(7.77)^x=(7.777)^y=1000. then prove 1/x-1/y=1/3

Dear Student
Please check the statement again it may be 77.7 but I have written down a solution. The approach will be similar 

$\frac{1}{x}-\frac{1}{y}=\frac{1}{3}(\log 7.77 - \log 7.777)$
log7.77 - log7.777  will come out to be 1   // you need to check underlined number