Does my license allow multiple users on one Mac?

You bet! Here's the pertinent piece of the LogTen Pro license agreement:

Coradine grants to you the non-exclusive, limited right to install and use the Coradine software program downloaded or contained on the CD-ROM or disk (the "Software"). The license permits either (a) multiple users to install and use the Software on a single machine; or (b) a single user to install and use the Software on multiple machines. However, a single license does not allow multiple users to ever use Software on multiple machines, regardless of whether such use is concurrent.

Using LogTen Pro X with multiple users

LogTen Pro X is a “shoebox” app, like Apple’s iPhoto, or iTunes. Everything about LogTen Pro including its preferences, reports, images, etc. is stored in the applications "container" located in your home directory at: ~/Library/Containers/com.coradine.LogTenProX

In Mac OS X 10.7 "Lion" and later the Library folder is hidden, you can find it easily by holding down the option key when selecting the Go menu in the Finder.

To use LogTen Pro X with multiple users, you will need to also have multiple user accounts on the Mac under Lion. For more information see: About User and Group Accounts and the Set up users on your Mac help documents from Apple.