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If their immigration system is computerized, your name will be in the system with the passport number registered against  it, then you need to leave and enter on the same passport. You can take the risk but that is up to you, but using the other passport they could then detain you at the airport.

Have you thought of contacting a Russian Embassy for information ??

Thanks so much... Yes, I am contacting some embassies but they redirect me to migration because they are the ones in charge of that.

I was told the following (best explained by an example):

Let's say you have a German and Russian passport and you use your Russian passport to get into Russia. In an emergency  the German authorities can not help you because you are travelling in Russia as a Russian national. If you used your German passport you are entitled to their help in a crisis situation.
This is what I have been told... but please confirm with the relevant authorities/embassies, things might have changed and different countries might have different rules.

In any case it is not unimportant what passport you use when you enter and leave a country!