Problem installing mysql server on 18.04

[Colin Law]

I have installed mysql-server and then run
sudo mysql_secure_installation
which prompts me to enter a root password.

I then run
mysql -u root -p
and get prompted for the pasword but then I get
Access denied for user 'root'@'localhost'

I have gone round a couple of times being ultra careful with the pwd entry
to no avail.  The log below shows a server restart and login attempt and I
can't see anything wrong.

Any suggestions gratefully received.

Colin

2018-07-01T11:05:15.498133Z 0 [Warning] TIMESTAMP with implicit DEFAULT
value is deprecated. Please use --explicit_defaults_for_timestamp server
option (see documentation for more details).
2018-07-01T11:05:15.499689Z 0 [Note] /usr/sbin/mysqld (mysqld
5.7.22-0ubuntu18.04.1) starting as process 15056 ...
2018-07-01T11:05:15.504173Z 0 [Note] InnoDB: PUNCH HOLE support available
2018-07-01T11:05:15.504224Z 0 [Note] InnoDB: Mutexes and rw_locks use GCC
atomic builtins
2018-07-01T11:05:15.504230Z 0 [Note] InnoDB: Uses event mutexes
2018-07-01T11:05:15.504235Z 0 [Note] InnoDB: GCC builtin
__atomic_thread_fence() is used for memory barrier
2018-07-01T11:05:15.504240Z 0 [Note] InnoDB: Compressed tables use zlib
1.2.11
2018-07-01T11:05:15.504246Z 0 [Note] InnoDB: Using Linux native AIO
2018-07-01T11:05:15.504491Z 0 [Note] InnoDB: Number of pools: 1
2018-07-01T11:05:15.504586Z 0 [Note] InnoDB: Using CPU crc32 instructions
2018-07-01T11:05:15.506091Z 0 [Note] InnoDB: Initializing buffer pool,
total size = 128M, instances = 1, chunk size = 128M
2018-07-01T11:05:15.514132Z 0 [Note] InnoDB: Completed initialization of
buffer pool
2018-07-01T11:05:15.516438Z 0 [Note] InnoDB: If the mysqld execution user
is authorized, page cleaner thread priority can be changed. See the man
page of setpriority().
2018-07-01T11:05:15.528769Z 0 [Note] InnoDB: Highest supported file format
is Barracuda.
2018-07-01T11:05:15.583667Z 0 [Note] InnoDB: Creating shared tablespace for
temporary tables
2018-07-01T11:05:15.583842Z 0 [Note] InnoDB: Setting file './ibtmp1' size
to 12 MB. Physically writing the file full; Please wait ...
2018-07-01T11:05:15.762178Z 0 [Note] InnoDB: File './ibtmp1' size is now 12
MB.
2018-07-01T11:05:15.763759Z 0 [Note] InnoDB: 96 redo rollback segment(s)
found. 96 redo rollback segment(s) are active.
2018-07-01T11:05:15.763783Z 0 [Note] InnoDB: 32 non-redo rollback
segment(s) are active.
2018-07-01T11:05:15.764577Z 0 [Note] InnoDB: Waiting for purge to start
2018-07-01T11:05:15.814863Z 0 [Note] InnoDB: 5.7.22 started; log sequence
number 2590746
2018-07-01T11:05:15.815213Z 0 [Note] InnoDB: Loading buffer pool(s) from
/var/lib/mysql/ib_buffer_pool
2018-07-01T11:05:15.815625Z 0 [Note] Plugin 'FEDERATED' is disabled.
2018-07-01T11:05:15.818372Z 0 [Note] InnoDB: Buffer pool(s) load completed
at 180701 12:05:15
2018-07-01T11:05:15.822701Z 0 [Warning] Failed to set up SSL because of the
following SSL library error: SSL context is not usable without certificate
and private key
2018-07-01T11:05:15.822750Z 0 [Note] Server hostname (bind-address):
'127.0.0.1'; port: 3306
2018-07-01T11:05:15.822771Z 0 [Note]   - '127.0.0.1' resolves to
'127.0.0.1';
2018-07-01T11:05:15.822823Z 0 [Note] Server socket created on IP:
'127.0.0.1'.
2018-07-01T11:05:15.833548Z 0 [Note] Event Scheduler: Loaded 0 events
2018-07-01T11:05:15.833993Z 0 [Note] /usr/sbin/mysqld: ready for
connections.
Version: '5.7.22-0ubuntu18.04.1'  socket: '/var/run/mysqld/mysqld.sock'
 port: 3306  (Ubuntu)
2018-07-01T11:05:26.799596Z 2 [Note] Access denied for user 'root'@
'localhost'
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