Answer:
x = -16/7
Explanation:
The equation as written reduces to finding the solution to a 7th-degree polynomial. The one real solution, found using a graphing calculator, is ...
x ≈ 1.60945071137
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Since this is beyond the scope of most algebra courses, we suspect you want the solution to ...
e^(x-2) = (1/e^6)^(x+3)
x -2 = -6(x +3) . . . . . . . . take the natural log of both sides
x -2 = -6x -18 . . . . . . . . . eliminate parentheses
7x -2 = -18 . . . . . . . . . . . add 6x
7x = -16 . . . . . . . . . . . . . add 2
x = -16/7