ork has a signal output of 40 V and a loss of 6 dB. What is the input signal voltage? (Equal impedances assumed.) -6 dB = 20 log 40/X. We shortcut this procedure by remembering our 10 log values. With a voltage or amperage relationship, the dB value is double (20 is twice the magnitude of 10). The value of X is 80 V. Whereas in our 10 log regime 3 dB doubled (or halved), here 6 dB doubles or halves. A more straightforward way of carrying out this procedure will be suggested in the next section. X can be directly calculated. C.5 CALCULATING A NUMERIC VALUE GIVEN A dB VALUE The essence of the problem of calculating a numeric value given a dB value can be stated as such: If we are given the logarithm of a number, what is the number? To express this, two types of notation are given in the literature as follows: (1A) log-1 0.3010 (2A) log- 2=100, (1B)antilog(0.3010) (2B)antilog2 =100. In the case of example 1, the logarithm is 0.3010, which corresponds to the number 2. If we were to take the log (base 10) of 2, the result is 0.3010. In example 2, the log of 100 is 2 or, if you will, 2 is the logarithm of 100. For our direct application we may be given a decibel value and be required to convert to its equivalent numeric value. If we turn to our introductory comments, when dealing in the power domain, we know that if we are given a decibel value of 20 dB, we are working with a power gain or loss of 100; 23 dB, 200; 30 dB, 1000; 37 dB, 5000; and SO on. A scientific calculator is particularly valuable when we are not working directly with multiples of 10. For instance, enter the logarithm of a number onto the calculator keypad and the calculator can output the equivalent numeric value. Many hand-held scientific calculators use the same button for the log as for the antilog. Usually one can access the antilog function by first pressing the "2nd" button, something analogous to upper case on a keyboard. Often printed directly above the log button is "10x." On most calculators we first enter the logarithm on the numerical key