<Dd> gain - db = 10 log ⁡ (I out 2 R out I in 2 R in) dB . (\ displaystyle (\ text (gain - db)) = 10 \ log (\ left ((\ frac (I_ (\ text (out)) ^ (2) R_ (\ text (out))) (I_ (\ text (in)) ^ (2) R_ (\ text (in)))) \ right)) ~ (\ text (dB)).) </Dd> <P> In many cases, the input and output impedances are equal, so the above equation can be simplified to: </P> <Dl> <Dd> gain - db = 10 log ⁡ (I out I in) 2 dB, (\ displaystyle (\ text (gain - db)) = 10 \ log \ left ((\ frac (I_ (\ text (out))) (I_ (\ text (in)))) \ right) ^ (2) ~ (\ text (dB)),) </Dd> </Dl> <Dd> gain - db = 10 log ⁡ (I out I in) 2 dB, (\ displaystyle (\ text (gain - db)) = 10 \ log \ left ((\ frac (I_ (\ text (out))) (I_ (\ text (in)))) \ right) ^ (2) ~ (\ text (dB)),) </Dd>

An amplifier has voltage gain of 50. this gain in db will be