Answer:
x=-9
Explanation:
(square root 6)^8x= 216^(x-3)
Rewriting sqrt(6) as 6^1/2
6^1/2^8x = 216^(x-3)
We know a^b^c = a^(b*c)
6^(1/2*8x) = 216^(x-3)
6^(4x) = 216^(x-3)
We know 216 = 6^3
6^(4x) = 6^3^(x-3)
We know a^b^c = a^(b*c)
6^(4x) = 6^(3*(x-3))
6^(4x) = 6^(3x-9)
Since the bases are the same, the exponents have to be the same
4x = 3x-9
Subtract 3x from each side
4x-3x =3x-3x-9
x = -9