To solve for x in the equation 49^(1-2x) = 343, we need to rewrite 343 as a power of 7, since 49 and 343 are both powers of 7.

Notice that 343 is equal to 7^3.

Therefore, we can rewrite the equation as:

7^2(1-2x) = 7^3

Now we can simplify by multiplying the exponent 1-2x by 2:

7^2 - 4x = 7^3

49 - 4x = 343

Subtract 49 from both sides:

-4x = 294

Now divide by -4:

x = -73.5

Therefore, x = -73.5.