I had success using jdbcdslog.  As @Saeed Zarinfam mentioned here, Play 2.5 includes this by default. 
Unlike this answer, this solution shows the parameter values instead of question marks.
Here are the steps I followed to get it working for Play 2.4 and MySQL: 
Add to build.sbt:
"com.googlecode.usc" % "jdbcdslog" % "1.0.6.2"
Add to logback.xml:
<logger name="org.jdbcdslog.StatementLogger"  level="INFO" /> <!-- Will log all statements -->
Create conf/jdbcdslog.properties file containing:
jdbcdslog.driverName=mysql
jdbcdslog.showTime=true
Change db.default.url (example):
jdbc:mysql://127.0.0.1:3306/mydb
changes to
    jdbc:jdbcdslog:mysql://127.0.0.1:3306/mydb;targetDriver=com.mysql.jdbc.Driver
Change db.default.driver:
org.jdbcdslog.DriverLoggingProxy