Show an alternative logo on Kickstart blog page and blog posts (a logo-alt.png file - of the same dimensions as the original logo - must be uploaded to the images folder in the theme folder)

style.css

/* Logo, hide text */

/* Existing CSS for reference */
.header-image .site-header .wrap {
	background: url(images/logo.png) no-repeat left center;
	padding: 0;
}

/* Show alternate logo on Date archives */
.header-image.page-template-page_blog .site-header .wrap,
.header-image.single-post .site-header .wrap {
	background: url(images/logo-alt.png) no-repeat left center;
}

/* Now go to the block where responsive styles are found */
@media only screen and (max-width: 900px) {
	
	/* Find the code block below and add the .header-image.page-template-page_blog and .header-image.single-post lines to it */
	
	/* Reset alterative logo back to regular logo for responsive menu */
	.header-image .site-header .wrap,
	.header-image.page-template-page_blog .site-header .wrap,
	.header-image.single-post .site-header .wrap {
		/* Whatever styles are already in here */
	}

}