(0,5)^5-x = 16√2
0,03125^5-x = 16√2
(0,03125)^-x = 16√2
(-x) * log(0,03125) = log(16√2)
x = -log(16√2) / log(0,03125)
x ≈ 7,347

(1/3)^5x-1 + (1/3)^5x = 36
(1/3)^(5x-1) + (1/3)^(5x) = 36
(1/3)^(5x-1) (1 + 1/3) = 36
(1/3)^(5x-1) (4/3) = 36
(1/3)^(5x-1) = 36 * 3/4
(1/3)^(5x-1) = 27
5x-1 = log(27) / log(1/3)
5x-1 = 3
5x = 4
x = 4/5

53^2x + 715^x - 65^2x = 0
53^(2x) + 715^x - 65^(2x) = 0
59^x + 715^x - 625^x = 0
53^x 3^x + 73^x 5^x - 65^x 5^x = 0
53^x 3^x + 73^x 5^x - 65^(2x) = 0
53^x 3^x + 73^x 5^x - 65^(2x) = 0
15^x + 353^x - 150^x = 0
(15^x - 125^x) + 353^x = 0
(3^x)^2 - 5^x)^2 + 353^x = 0
[(3^x - 5^x) + 35]/35 = 0
3^x - 5^x = -35/35
3^x - 5^x = -1
No real solutions.