Profile: TechnoteNitesh

If you want the logo just beside the text then it could be achieved by the following code:

<a href="@Url.RouteUrl("HomePage")">
    <img class="menu-img" alt="#" src="Your logo">
</a>

.header-menu .menu-img {
  display: none;
}

@media all and (min-width: 1001px) {

.header-menu.stick {
  display: block;
  position: fixed;
  top: 0;
  left: 0;
  right: 0;
  background: #fff;
  padding: 11.5px 0;
  text-align: center;
  box-shadow: 0 8px 8px rgba(0,0,0,.085);
}
.header-menu>ul {
  display: block;
  width: auto;
}
.header-menu.stick .menu-img {
  display: block;
 margin-bottom: -35px; 
  margin-left: 301px;

}

}

Re-size the logo to 100px x 39px resolution.
You can adjust the margin-bottom and margin-left according to your need.

P.S. The bold text is what you've to add to the above mentioned code.

Regards.

Pramil Gawande
+91 7755902019
Technote Software Solution Pvt. Ltd.