You may be wondering, how is it OK to connect a 3.3V chip like the TSL2561 to 5.0V data pins like the Arduino? Isn't that bad? Well, in this specific case its OK. I2c uses pullup lines to the 3.3V power pin, so the data is actually being sent at 3.3V. As long as all the sensors/device on the i2c bus are running on 3.3V power, we're fine.
However, don't use a 5.0v powered i2c device (like the DS1307) with pullups at the same time as a 3.3V device like the TSL2561! If you want to use this sensor with a datalogger that uses the DS1307, remove any/all of the pullup resistors from the DS1307 SDA/SCL pins. The pullups built into the TSL2561 will then be active and keep the voltage at 3.3V which is safe for both the RTC and the sensor.
Does this mean I just remove the resistors then use the data logger as normal?
Thanks in advance for the help!