Finding root password on new 5.7 install

[CHARLES WANGERSKY]

It appears that the MySQL 5.7 installer for Mint Linux does not like to install with a blank password, instead generating a random password for 'root' and copying that into a log file that I cannot locate. (TechRepublic says /var/log/mysqld but there is no such file on Mint.) I have tried to reset the root password with no luck; last thing I tried, after forcing a clean install, was

sudo mkdir /var/run/mysqld
sudo chown mysql /var/run/mysqld
sudo --user=mysql mysqld_safe --skip-grant-tables --skip-networking &
mysql -u root mysql
mysql> update user set authentication_string=PASSWORD('somepassword') where user='root';
mysql> flush privileges;
mysql> quit;

The update returned "1 row changed, 0 errors, 1 warning' but didn't say what the warning was. After this, I found I could not stop mysqld_safe, so I rebooted; but at that point I found that the password I had set did not work.

What am I doing wrong? Is there any way to set that password, or do I abandon MySQL for something else?