I would expect the answer to be positive, but it appears otherwise for some values of $x \geq 1$.
Here is a simple C++ code that I have used in order to test this:
#include <complex>
#include <iostream>
void test(double x)
{
complex<double> i(0,1);
complex<double> res1 = (2*x-1)*log(i*i);
complex<double> res2 = log(pow(i*i,2*x-1));
cout<<res1<<endl;
cout<<res2<<endl;
}