We assume you mean
[tex]\ \ \display{16=4^{3x-7}}[/tex]
This is solved by writing 16 as a power of 4 and equating exponents.
[tex]\ 4^{2}=4^{3x-7}[/tex]
2 = 3x - 7 . . . . . equate exponents
9 = 3x . . . . . add 7
3 = x . . . . . divide by 3
The solution is x = 3.
