If I grasp the gist of your inquiry correctly, it appears that you're endeavoring to incorporate a logo into a responsive bootstrap 4 template. If my assumption is on point, substituting the following line:
<img class="img-fluid picture-padding" src="temp" alt="temp">
With:
<a class="navbar-brand" href="#">
<img src="temp" width="30" height="30" alt="">
</a>
Should achieve the desired outcome.
Below is the complete code for the bootstrap 4 template page utilized:
<!doctype html>
<html lang="en">
<head>
<!-- Required meta tags -->
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
<!-- Bootstrap CSS -->
<link rel="stylesheet" href="https://stackpath.bootstrapcdn.com/bootstrap/4.1.3/css/bootstrap.min.css" integrity="sha384-MCw98/SFnGE8fJT3GXwEOngsV7Zt27NXFoaoApmYm81iuXoPkFOJwJ8ERdknLPMO" crossorigin="anonymous">
<title>Hello, world!</title>
</head>
<body>
<nav class="navbar navbar-expand-md bg-dark navbar-dark sticky-top">
<!-- <a class="navbar-brand" href="#">Logo</a> -->
<a class="navbar-brand" href="#">
<img src="./test.png" width="30" height="30" alt="">
</a>
<button class="navbar-toggler" type="button" data-toggle="collapse" data-target="#collapsibleNavbar">
<span class="navbar-toggler-icon"></span>
</button>
<!-- Links -->
<div class="collapse navbar-collapse" id="collapsibleNavbar">
<ul class="navbar-nav">
<li class="nav-item">
<a class="nav-link" href="#">Link 1</a>
</li>
<li class="nav-item">
<a class="nav-link" href="#">Link 2</a>
</li>
<li class="nav-item">
<a class="nav-link" href="#">Link 3</a>
</li>
</ul>
</div>
</nav>
<!-- Optional JavaScript -->
<!-- jQuery first, then Popper.js, then Bootstrap JS -->
<script src="https://code.jquery.com/jquery-3.3.1.slim.min.js" integrity="sha384-q8i/X+965DzO0rT7abK41JStQIAqVgRVzpbzo5smXKp4YfRvH+8abtTE1Pi6jizo" crossorigin="anonymous"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/popper.js/1.14.3/umd/popper.min.js" integrity="sha384-ZMP7rVo3mIykV+2+9J3UJ46jBk0WLaUAdn689aCwoqbBJiSnjAK/l8WvCWPIPm49" crossorigin="anonymous"></script>
<script src="https://stackpath.bootstrapcdn.com/bootstrap/4.1.3/js/bootstrap.min.js" integrity="sha384-ChfqqxuZUCnJSK3+MXmPNIyE6ZbWh2IMqE241rYiqJxyMiZ6OW/JmZQ5stwEULTy" crossorigin="anonymous"></script>
</body>
</html>
Here is the mobile output:
https://i.sstatic.net/RveeL.png
And here is how it displays on desktop:
https://i.sstatic.net/aut0Y.png