How to rotate a local axis of an object to another object?

Using the following code I can rotate the local Z axis to another GameObject.

 /// <summary>
 /// Faces local Z axis to another target object.
 /// </summary>
 /// <param name="target">Target.</param>
 private void FaceTo(GameObject target){
     float damping = 0.03f;
     var lookPos = target.transform.position - transform.position;
 
     var rotation = Quaternion.LookRotation(lookPos);
 
     transform.rotation = 
          Quaternion.Slerp(transform.rotation, rotation, Time.deltaTime * damping); 
 }

the result during the Update method is the following:

Now I need to face to the object using another axis, not the Z axis of my object; for example I would use the positive X axis for obtain this result:

How can I modify my script? Unfortunately I do not know the math of Quaternions and Vectors and I'm a bit confused.