Bootstrap 3 Fixed Nav - Hide/Resize Logo - css

Question

Using the latest version Bootstrap, I am wanting to replace the branding area text with a logo. On my desktop, it looks perfect, on my iPhone, the logo appears under the small collapse menu, whereas it should be beside it (to the left of it). If I make the logo smaller, it works fine on the iPhone, but the small logo is too small for the desktop site. I thought by adding the img-responsive class to the logo, it would shrink accordingly, but that fails. If you want to replicate this, the logo is 276px wide 40px high.
Everything appears fine on the iPhone in horizontal orientation (it is strictly a problem when viewing in vertical, which is naturally the way most people hold their phone).
Here is the related code (you will notice near the bottom, there is a purchase button, this automatically gets hidden on the iPhone, which would suffice for the logo if there is no other option). Mind, the ultimate solution would be to have the logo shrink based on screen size.
<!-- Fixed navbar -->
<div class="navbar navbar-default navbar-fixed-top">
<div class="container">
<div class="navbar-header">
<button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-collapse">
<span class="icon-bar"></span>
<span class="icon-bar"></span>
<span class="icon-bar"></span>
</button>
<a class="navbar-brand" href="index.php"><img class="img-responsive" src="img/logo.png" alt=""></a>
</div>
<div class="navbar-collapse collapse">
<ul class="nav navbar-nav">
<li class="active">Home</li>
<li class="dropdown">
Application <b class="caret"></b>
<ul class="dropdown-menu">
<li>Features</li>
<li>Screenshots</li>
<li>Demos</li>
<li class="divider"></li>
<li>Purchase</li>
<li>Licensing Model</li>
</ul>
</li>
<li class="dropdown">
Documentation <b class="caret"></b>
<ul class="dropdown-menu">
<li>Version Info</li>
<li>System Requirements</li>
<li class="divider"></li>
<li>Installation Guide</li>
<li>Integration Guide</li>
<li>Frontdesk Manual</li>
</ul>
</li>
<li class="dropdown">
Support <b class="caret"></b>
<ul class="dropdown-menu">
<li>Knowledgebase</li>
<li>Submit Ticket</li>
<li>View Ticket Status</li>
<li class="divider"></li>
<li>Installation Service</li>
<li>Development Services</li>
</ul>
</li>
<li class="dropdown">
Contact <b class="caret"></b>
<ul class="dropdown-menu">
<li>Presales Questions</li>
<li>Contact Us</li>
</ul>
</li>
<li class="dropdown">
Legal <b class="caret"></b>
<ul class="dropdown-menu">
<li>Privacy Policy</li>
<li>Terms of Use</li>
<li>Site Security</li>
<li class="divider"></li>
<li>Money Back Guarantee</li>
</ul>
</li>
</ul>
<button type="button" class="btn btn-success" style="margin-top: 8px; margin-left: 30px;">Purchase</button>
</div>
<!--/.nav-collapse -->

Answer 1

This fixes the I-phone issue with the brand logo appearing under the collapsed menu icon. you might have to play with the width a bit depending on your setup:
#media (max-width: 500px) {
.navbar-brand{
width:60%;
}
}

Answer 2

Put your image as a background in css with background-size:cover.