Manual:$wgLogo

Details
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The URL of the site logo (i.e. the image displayed in the upper-left corner of the page in most MediaWiki installations). Either a fully-qualified URL or a relative path from DOCUMENT_ROOT.

If it's a relative path, it has to start with a slash (a file in DOCUMENT_ROOT is /file.png, not file.png).

The logo is expected to be 135 x 135 pixels. A bigger size can be used by modifying the site CSS (and smaller sizes are possible with no changes).

Note that if you use a bigger image, MediaWiki will not resize this image! Instead, the image will be cut off so that only part of it (the upper left-hand corner to be precise) will be visible.

If this corner is completely white, it might look like the image does not display although in fact it does.

Examples
Upload your logo file onto your server.

Let's say it ends up as /images/4/47/mylogo.png.

Then you can use it as your site logo by adding this line to LocalSettings.php:

Make sure that you add this line below the definition of $wgScriptPath! Otherwise, $wgScriptPath will still be undefined and the logo will not display.

Vary logo per language
With CSS, it is possible to use a different logo for each interface language: