An arbitrary resistor put in series with a voltage yields no attenuation, I believe what you are asking about is attenuation associated with a voltage divider, typically the attenuation assosicated with a series resistor followed by another resistor (or component with a frequency depedant reactance) which is usually a shunt to ground. You are concerned with the voltage at the junction of these 2 resistors.
For example -
Input via a 10k series resistor connected to a 50k shunt resistor to ground. The output voltage Vout = Vin( Rshunt/(Rshunt + Rseries))
and for this example Vout = Vin*(5/6)
You can convert that voltage ratio to dB with the equation
dB = 20*log(votage ratio) = 20*log(Rshunt/(Rshunt+Rseries)) =
20*log(5/6) = -1.583 dBv
You can get far better explanations by using google and entering 'voltage divider' which will offer discussion and calculators -
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/voldiv.htmland doing the same for 'decibel calculator'
http://www.mcsquared.com/dbframe.htmI'm sure there are calculators out there that combine both funtions, or its quite easy to do your own in Excel with the formulas above.
And all of the above is going to lead to yet more questions. And you don't want to use your balance control to do so.... Why? Just take your balance knob (assuming it has enough range) and adjust it on the shaft so what looks to be the 'balaced', equal. position has the degee of attenuation on the channel you require. We won't tell anyone. Mucking about with a set screw on a knob is a lot easier than adding attenuation.