Question

(1/27)^m×81^-n=243..express m in terms of n

Answer 1

Answer:

m = - (4n + 5)/3

Step-by-step explanation:

(1/27)^m×81^-n=243..express m in terms of n

(1/27)^m * 81^(-n) = 243

=> (1/3³)^m * (1/81)ⁿ = 243

=> (1/3³)^m * (1/3⁴)ⁿ = 3⁵

=> (1/3)^(3m) * (1/3)⁴ⁿ = (1/3)⁻⁵

=> (1/3)^(3m + 4n) = (1/3)⁻⁵

=> 3m + 4n = -5

=> 3m = -5 - 4n

=> m = - (4n + 5)/3