Problems with query where by means of select

in your view

 <form action="{{action('UsuarioController@show')}}" method="post">
                {{csrf_field()}}
                   <select name="tipo" id="tipo" class=" form-control"  value="{{ old('tipo') }}"  required>
                    @foreach($usuarios as  $usuario)
                      <option value="{{$usuario->usuario_ad }}">{{ $usuario->nombre }}</option>
                   @endforeach
               </select>
            <a class="btn btn-info" >Buscar</a>
         </form>

on your controller

$usuarios=usuarios::where("usuario_ad","=",$request->tipo)->get();
return  view('usuario.index',compact('usuarios'));

I hope it will help you or help you a bit in your logic

Good tests with this, since you are launching a POST route you need to access the request variable.

<form action="{{action('UsuarioController@show')}}" method="post">
  {{csrf_field()}}
  <select name="tipo" id="tipo" class=" form-control"  value="{{ old('tipo') }}"  required>
         @foreach($usuariosOpciones as $id => $usuario_ad)
         <option value="{{ $id }}">{{ $usuario_ad }}</option>
         @endforeach
  </select>
  <a class="btn btn-info" >Buscar</a>
 </form>

To access the value of the select, the select must be inside the "form" tags.

public function show(Request $request)
        {
            $usuarios=usuarios::where("usuario_ad","=",$request->usuario_ad)->get();
            $tipo = $request->tipo; //Para acceder a la variable del select
            return  view('usuario.index',compact('usuarios'));
        }