Question

(7.77)^x=(0.777)^y=1000 proved that 1/x-1/y=1/3​

Answer 1

Answer:

proved

Step-by-step explanation:

Given  (7.77)^x=(0.777)^y=1000 proved that 1/x-1/y=1/3​

Consider 7.77^x = 10^3

So 7.77 = 10^3/x---------1

Also 0.777^y = 10^3

0.777 = 10^3/y------------2

Dividing equation 1 by 2 we get

7.77 /0.777 = 10^3/x / 10^3/y

7770 / 777 = 10^3/x – 3/y (a^m / a^n = a^m – n)

10 ^1 = 10^3/x -3/y

W hen bases are same exponents are equal

3/x – 3/y = 1

1/x – 1/y = 1/3 (proved)