Solve the equation: 4 ^ x + 5 ^ x = 2 times (6 ^ x)

Solve the equation: 4 ^ x + 5 ^ x = 2 times (6 ^ x)

The equation has only one solution, x = 0
Let f (x) = (4 / 6) ^ x + (5 / 6) ^ x, through the derivative, we know that x = 0, f (x) max = f (0) = 2