Question

If (2.3)x = (0.23)y = 1000, show that 1/x - 1/y = 1/3

Answer 1

(2.3)x = (0.23)y = 1000

=> log10(2.3)x = log10(0.23)y = log10(103)

=> x log10(2.3) = ylog10(0.23) = 3

=> 3/x = log10 2.3, 3/y = log10 0.23

=> 3(1/x - 1/y) = 1

=> 1/x - 1/y = 1/3