###WAY #1 - cPanel###
I assume your host is using cPanel managing your Server.

Browse `domainname.com/cpanel`, login their with cPanel credential:<br>
![enter image description here][1]

Change the values according the following image:<br>
![enter image description here][2]

Add the redirection and you are done.

###WAY #2 - `.htaccess`###
Open up your `.htaccess` of `domainname.com/blog` in edit mode. Put the following code there (I made it using [RapidTables Redirect Generator](http://www.rapidtables.com/web/tools/redirect-generator.htm)):

    Redirect 301 /blog/ http://newdomainname.com

Save it. And *yala*!

  [1]: https://i.sstatic.net/vVGAR.png
  [2]: https://i.sstatic.net/v7PdF.png