Answer:
To solve the equation (3^{2x+4} = 9^{3x-4}), let's first simplify both sides.
Since (9 = 3^2), we can rewrite (9^{3x-4}) as ((3^2)^{3x-4}), which simplifies to (3^{2(3x-4)}).
So, the equation becomes:
3^{2x+4} = 3^{2(3x-4)}
Now, since the bases are the same (both are 3), we can equate the exponents:
2x + 4 = 2(3x - 4)
2x + 4 = 6x - 8
4 = 4x - 8
12 = 4x
x = 3
So, the value of (x) is (3).
