suddedenly increased in size of Log files form 32GB to 70 GB
A full database backup won't help your log size. 

Full Recovery Model means "Can restore to any point in time." - including before that new database backup was taken. 

Simple Recovery Model means "Can restore to the last database backup".

So... have a think about whether you need to restore to this morning or not (before your database backup). If you don't, then put your database into Simple Recovery Model, then back into Full. Then take a differential backup. Once you've done those three steps you will be able to recover to your last full database backup, the differential backup you just took, and any point in the future. Take regular log backups - try every ten-to-fifteen minutes.

And then look at your log. You should find it's mostly empty.

If not, look in sys.databases to see why it's not truncating. Other possible reasons include Replication that's broken, for example.