I'm not aware of another "service log book" other than inside the Owner's Manual. You can go to the regional official Yamaha website.. towards the bottom of the page you'll see "Yamaha Links", then "Owners Manuals". Plug in your bike's info and download a free PDF file. Or you can order a paper copy from any Yamaha Dealer , or from the website.. Under "Maintenance" you'll find "Owners Manuals". Same process for a Hard Copy.. for about $17 US.
You may also want to check your bike's VIN to see if any Yamaha "Safety Recalls" are outstanding. All safety recalls are free, it's for the bike so you do not have to be original owner, any Yamaha Dealer can perform the recall. Again go to the official Yamaha website for your part of the world (my US website won't work for you or I'd send the link). Bottom right.. see "Corporate Links" then "Factory Recalls".. Plug in the VIN and look for completed and or outstanding safety recalls.