If you're going to be wanting to log the data in the future, then I would assume you are going to need to feed the signal into an ADC for conversion into a digital form.
Because of that you might as well go that way from the start and not use the LM3914N.
You can scale and shift the incoming voltage so that the range you are interested in, plus the over voltage range, covers a range of (for instance) 0-5V (subtract 19V, scale the remainder down).
How do you do that? This answer will probably help you: https://electronics.stackexchange.com/a/18265/4245 - subtract 19V from the incoming voltage using a suitable op-amp. Then use a voltage divider to take that remaining voltage range down to the range of the ADC (3.3V, 5V, whatever).
You can then read the value from the ADC, log it, and display it on any LED display of your choice in any format you like, using any MCU that has the right IO options for you (the Arduino platform is a popular choice).
Once it's converted by the ADC you just have a set of numbers. It's then largely up to you how you divide those numbers up. Depending on your scaling resistors, ADC values (say, for a 10-bit ADC) from 0 to 900 could be 0% to 100% (19-48V) and displayed on an LED bargraph. The remaining 901-1023 would be "overvoltage" and could trigger a different LED to start blinking as a warning... The world is then really your oyster.
The equation given is a low frequency approximation that holds only when
$$\omega RC \ll 1 $$
The exact phasor equation for an RC 'differentiator' circuit is
$$V_{out} = \frac{j\omega RC}{1 + j\omega RC}V_{in}$$
Note that
$$V_{out} \le V_{in}$$
for all frequencies. However, when \$\omega RC \ll 1\$, we have that
$$V_{out} \approx j\omega RC\;V_{in} $$
which is the phasor equation for a differentiator. Since we've assumed \$\omega RC \ll 1\$ for this approximation, it follows that
$$V_{out} \ll V_{in}$$
for these frequencies in which the approximation holds.
Best Answer
You are looking for a window comparator. It can be implemented easily with a dedicated window comparator IC (like the TPS3700) or a dual comparator IC (or two single comparators). The two comparators should be open collector (i.e. not push-pull) so that the two outputs don't fight each other. Here's an example from the TLV170x comparator datasheet:
Since the two thresholds (you're using 4.5 V and 5.5 V) connect to the high impedance inputs of the comparators you don't have to buffer them. You can use a resistor divider, composed of three resistors in order to set two thresholds, from your supply voltage to ground. The datasheet for the aforementioned TPS3700 shows this:
In the event that the comparator supply voltage \$V_\text{S}\$ is less than your input thresholds you can divide down your the thresholds and your signal to less than \$V_\text{S}\$. For example, if you have \$V_\text{S} = 2\text{ V}\$ then you can divide your 4.5 V and 5.5 V thresholds by, say, 4 -- that would give you thresholds of 1.125 V and 1.375 V.