In your header.php which you copied into your child theme, replace the logo request with this:
If (is_front() || is_home) {
//Your logo for the front page
}Else {
// Your other logo
}
If your home page is static use is_front. If your home page is blogs use is_home.
I looked up your theme “classify”. If it’s the one from themeforest login to your themeforest and download the complete theme folder not just the WordPress install file. In the file you downloaded you’ll find the “classify-child.zip” install that as well into your WordPress theme. this will make a copy of the theme that you can customize but won’t be affected when you update the actual classify WordPress theme next time.
Now, from the classify folder, copy the header.php file into the classify-child folder in your wordpress install. Make the changes in the new header.php file that is in your classify-child theme.