No, x is not 1. This is because of domain restrictions on the logarithm's base
is equivalent to
cannot be one because 1 raised to any power is always 1
There are infinitely many values of x.
No doubt someone else knows better notation than me for that - what it says is that x can be any real number greater than 0 which is not 1.
is a valid solution for example
edit: about the X and x I was asking because they are generally taken as different variables although if they were different there'd be no way of solving the equation.
edit 2: the k is just being used as an example to demonstrate the log power law, it is unrelated to the question you ask. k is often used to denote a constant