Verified answer

81^x+1 = (27^3x) / (9^21/2)

(3^4)^(x+1) = (3^3)^3x / (3^2)^(21/2)

4(x + 1) = 9x - 21

4x + 4 = 9x - 21

5x = 25

x = 5

81^(x + 1) = (27^3x) / (9^21/2)

(27^3x) / 81^(x + 1) = (9^21/2)

(3^9x) / 3^(4x) = 3^4 (3^21)

3^5x = 3^25

5x = 25

x = 5

(3^4)^(x+1) = [(3^3)^(3x)]/[(3^2)^(21/2)] =>

3^(4x + 4) = 3^(9x - 21) =>

4x + 4 = 9x - 21 =>

25 = 5x =>

x = 5.