If for x , y ∈ R , x > 0 , y = log 10 x + log 10 x 1 / 3 + log 10 x 1 / 9 + … upto ∞ terms and 2 + 4 + 6 + … + 2 y 3 + 6 + 9 + … + 3 y = 4 log 10 x , then the ordered pair x , y is equal to

Step-by-step solution

2 + 4 + 6 + … + 2 y 3 + 6 + 9 + … + 3 y = 4 log 10 x 2 1 + 2 + 3 + - - - - y 3 1 + 2 + 3 + - - - - y = 4 log 10 x log 10 x = 6 x = 10 6 Now y = log 10 x + log 10 x 1 3 + log 10 x 1 9 - - - ∞ = 1 + 1 3 + 1 9 - - - ∞ log 10 x = 1 1 - 1 3 log 10 x = 9 So, x ,   y = 10 6 ,   9