Solve the following equation algebraically. 9^ (x-2) = (1/27) ^ (x+4)

Create equivalent expressions in the equation that all have equal bases. 3 2 (x+2) = 3 - 3 (x+12) 3 2⁢ x+2 = 3 - 3 ⁢ x+12 Since the bases are the same, then two expressions are only equal if the exponents are also equal. 2 (x+2) = - 3 (x+12 Simplify the left side. 2x + 4 = - 3 (x+12) 2⁢x + 4 = - 3 ⁢ x + 12

Simplify the right side. 2x + 4 = - 3 x - 36 2⁢x + 4 = - 3 ⁢x - 36

x = - 8