Question

(2.3)^x=(0.23)^y=1000, find the value of 1/x-1/y?

Answer 1

2.3^x = 0.23^y  = 1000

Apply logarithms:
    x Log 2.3 = y Log 0.23 =  Log 1000
    x Log 2.3  = y  (Log 2.3/10 ) = 3
    x Log 2.3   = y (Log 2.3 - Log 10) = 3

1/x = (Log 2.3)/3  
1/y = (Log 2.3 -1)/3 = (Log 2.3)/3  - 1/3
1/y = 1/x - 1/3

1/x - 1/y = 1/3