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 2017
class=com.android.repository.impl.installer.BasicInstaller
path=C\:\\Users\\user\\AppData\\Local\\Temp\\PackageOperation03

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

I got the same issue on Linux. It was a permission issue on the SDK installation folder.

In Tools -> Android -> SDK manager there is the SDK installation folder at the top of the window.

Just do a chmod 777 -R on this folder, problem solved.