The logs are common or natural?
Also that is not the equation you gave in post #664. In post #664 you gave this equation
log(x+1) - 2logx^2=1
That is the equation I said does not have a root of 1 / 3.
Now you are giving this equation.
This is it;
log(x^2 + 1) - 2logx = 1
They are not the same.