If you see a blankpage after updating from Joomla 2.5.8 to Joomla 3.4.8 it is probably due to one of the following issues.
- The Joomla Template you were using before is not Joomla 3 compatible.
- The Modules/Extensions you have installed are not Joomla 3 compatible.

To Update your Joomla Template and Modules after updating your site from Joomla 2.5.8 to Joomla 3.4.8
Note: I do this in Cpanel file Manager or through Ftp. Use whatever suits you best.
1: Navigate to the folder you have your Joomla installation in.
- If your site is at Example: www.mywebsite.com then your Joomla Installation would be in your Public_html folder.
- If your site is at Example: www.mywebsite.com/joomlasite then your Joomla Installation would be in your Public_html/joomlasite folder.

Updating Template to Joomla 3 Version
1: In your Joomla website installation navigate to the /Templates folder.
2: Delete the existing template.
3: Now upload the Joomla 3 version of your template to the /Templates folder.

Updating Modules to Joomla 3 Version
1: In your Joomla website installation navigate to the /Modules folder.
2: Delete any existing modules you had installed in Joomla 2.5.
3: Now upload the Joomla 3 versions of the modules to the /Modules folder.

Open your Web Browser and now check your Joomla site. Is it loading properly. Fingers crossed it is.
Note: You may need to clear your browsers cache a couple of times to refresh the site properly. Do this by holding down CTRL-R or by pressing the F5 function key.

Good Luck with your updating.