How to tell vacuum tube is gone bad??

I recently purchased primaluna prologue 3 and I connect with dynaudio bm6a.

First I saw is lights of three vacuum tubes are dim and

other lights of three vacuum tubes are bright.

Among 6, 1 of vacuum tube has little soot on wall.

When I connect output-2 with bm6a speaker (active speaker), the volume is very low even I tune max volume.

When I connect output-1 with the speaker, the volume is loud enough with 1/3 of preamp volume.

Are these symptom indicated bad vacuum tubes?

Any other way to check vacuum tube??
Hard to tell with this scenario. You will need a tube tester and test the tube for emissions and a life test to verify the tube operating within spec.

I'm not familiar with the amplifier but if you move the tube to the opposite channel and perform the same output test on the left/right channels to verify the problem moved with the tube. Otherwise the problem may be in the circuit for that tube location, resistor most likely but the circuit will need testing to verify which component is out of spec.

The Primaluna Prologue 3 has 2 sets of pre outs labeled 1 and 2. Is the problem actually output 1 and output 2, or is the problem a difference between L and R outputs?
Posting twice is good.
"How to tell vacuum tube is gone bad??"

Try the tubes in a friends amp. If nothing bad happens its probably safe to put them in your amp.