49^(×)+7^(×)=686?

7^x + 49^x = 686
7^x + 7^(2x) = 2 * 7^3
1 + 7^x = 2 * 7^(-x+3)
-1 = -2 * 7^(-x+3) + 7^x

And Maxima came up with 2 solutions:

x = 1 / log(7) * (log ( 1/2 + 3/2 * sqrt (305)) + iπ )

and in the realm of reals:

x = 1 / log(7) * log ( -1/2 + 3/2 * sqrt (305))

x ≈ 1.668293824