Will two separate 50db sounds together constitute a 100db sound explain mathematical

Putting together two distinct 50 dB sound, do not create a 100 dB sound. Since decibels are logarithm of energy, creating two sounds together only makes the energy increase but the logarithm only goes up by somehow little. So increasing the sound by 10 dB, only makes it 10000 times louder because each 10 dB increase in sound makes the sound 10 times louder.

Twice as loud is an increase of 10Log (2) = 3.01 dB. So, 53,01 dB is twice as loud as 50dB.