This is a bit clumsy. First of all, you should be selecting your logo on how it should suit most/all pages, which in your case should be all subpages. For the home page, you are using "intro" plugin, which includes settings to have a semi-transparent background behind the logo so that it stands out better when placed on top of an image. This should be the logical approach.
You can't just "change" the logo <img> automatically when navigating pages, as it's a fixed element. The only way, would be to assign the logo as a background image in CSS, and then adjust the background-image source depending on what page you are on. Something like this:
.logo img {
visibility: hidden; /* must hide the original <img> logo but keep its size */
}
/* add the logo as a background image */
/* use the one that should go for all subpages */
.logo {
background-image: url(https://kgallery.b-cdn.net/content/custom/logo/kog-photogallery25a.png);
background-size: contain;
background-repeat: no-repeat;
background-position: 50%;
}
/* change the source for the index home page */
.page-index .logo {
background-image: url(https://kgallery.b-cdn.net/content/custom/logo/HOMEPAGE.png);
}
This should work, although it's not tried and tested for all possible scenarios.