You want to solve (4x-1)^=343.
I'm guessing here that that expression should be:
(4x-1)^n=343
where n is some value.
And since 343 = 7^3, I'm going to guess further that the original expression should have been:
(4x-1)^3=343
So, what we have is,
(4x-1)^3=7^3, or
(4x-1) = 7
4x = 8
x = 2
Answer: x = 2