Installation did not complete successfully. see the IDE log for details - Android studio

I had the same problem but starting the Android Studio in Administrator Mode has helped me to continue with the update.

The reason is that the SDK manager would write the location of the temp file where it downloads the installer. For example in OP's case its mentioned as below:

in a line form the log or error message

Due to some reason that file might not be available any more and Android studio instead of asking for a re-download would give this error.

The solution to fix this is to find the file .installData from where SDK manager is getting this info and delete it. This will force SDK manager to re download that component only and you don't need to download the complete SDK again

The content of the file looks something like this

#Tue May 16 18:41:10 GST 2017class=com.android.repository.impl.installer.BasicInstallerpath=C\:\\Users\\user\\AppData\\Local\\Temp\\PackageOperation03

The content and path of the file would be different for different components

I had the same problem and i tried to uninstall/install the android studio but that didn't work out for me.I had recently installed a fresh copy of windows. I'm using windows 10 64bit.My problem turned out to be permission for the folder that contained the android studio/sdk.To solve it, I removed old user permissions for user of old windows and added full control for my new user(not sure but i think modify permission would be enough).To do so, I right click on the folder then selected the security tab.

Then click on Edit

Then click Add in the new screen

my user is named hany so i wrote hany then clicked on Check Names and it choose the right one.Click Ok

the user appears as Users (DESKTOP-8FKNNEM\Users) and then i check the Full control Then Ok

If the user had already existed in the Security tab then it should have permissions that would enable writing