###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]

Don't forget to check the "Wildcard Redirect" to redirect all the subfolder/subpages also (*Thanks to @RobertHue*). *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 [WebConfs.com Redirect Generator](http://www.webconfs.com/htaccess-redirect-generator.php)):

    Options +FollowSymLinks
    RewriteEngine on
    RewriteRule (.*) http://newdomainname.com/$1 [R=301,L]

Save it. And *yala*!

##EDIT##
That's well said by @RobertHue. I did not mention the subfolder or subpages redirection. So I edited my answer, changed the attached images and posted new code. Thanks a lot @RobertHue for pointing the important things.


  [1]: https://i.sstatic.net/vVGAR.png
  [2]: https://i.sstatic.net/T93CH.png