updating a field based on relationship between 2 mysql tables

I have 2 mysql tables woith the following:

table_a

id, retailer_message, logos_id

logos

id, name

table_a has a retailer_message field, with records such as 'On sale at Amazon' logos table has records with the name field as 'Amazon' for example.

Now what I want to do, is update the table_a logos_id based on the relationship with the logos table.

So the following example

table_a

id, retailer_message, logos_id
1, On sale at Amazon
2, On sale at Asda

logos

id, name
1, Amazon
2, Misco
3, Asda
4, Tesco

This would then update the table_a and insert the logos_id of 1 and 3 respectively.

Could someone provide an SQL snippet to achieve this?

Thanks

If you always have the same message as the beginning of the message ("On sale at ") you can use something like this:

update table_a set logos_id = (select id from logos where name = substring(retailer_message,12));