From codex:
The the_author_meta Template Tag displays the desired meta data for a
user. If this tag is used within The Loop, the user ID value need not
be specified, and the displayed data is that of the current post
author. A user ID can be specified if this tag is used outside The
Loop.If the meta field does not exist, nothing is printed.
NOTE: Use get_the_author_meta() if you need to return (not display)
the information.
So, replace the_author_meta()
with get_the_author_meta()
. You can then use wp_get_attachment_image() to get an image element ready for outputting to the page.
<?php
$id = get_the_author_meta('author_logo');
if ($id) {
echo wp_get_attachment_image($id);
}
?>