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If you log into your Joomla 3.x administrator interface and see the following message near the top of your screen:

Error  "We have detected that your server is using PHP 5.3.29 which is obsolete and no longer receives official security updates by its developers. The Joomla! Project recommends upgrading your site to PHP 5.6 or later which will receive security updates at least until 2018-12-31. Please ask your host to make PHP 5.6 or a later version the default version for your site. If your host is already PHP 5.6 ready please enable PHP 5.6 on your site's root and 'administrator' directories – typically you can do this yourself through a tool in your hosting control panel, but it's best to ask your host if you are unsure."

Most cPanel hosting will have a PHP Version Manager icon on it's 1H Software section.  Simply click on it.  You want to select the root folder for your Joomla installation.  If you have only one domain that you're hosting, you can choose the public_html near the top.  Right next to it, you will see the version that your website is currently running on.

PHP Version Manager on cPanel hosting

Choose the 7.0.xx version, and click save.

Now go back to your website, and check both the front and back (administrator) areas and make sure everything is working correctly.

If I built your website, very good chance everything will be fine.  

If it isn't working correctly, simply go back and revert to an earlier version.  Then, go through your components, modules, and plugins and make sure everything is updated to the latest version.