I've read that plugging a bass guitar into a guitar amplifier is not advisable as it can fry the speaker. However, could a pre-amplifier solve this problem (adjusting output power and impedance). I'm aware that sound quality might not be the best as bass guitar output frequencies are lower than those a guitar amplifier is used to get.
The basic problem with a bass guitar in a guitar amp is that speaker and cabinet are not built for the low frequencies of the bass guitar.
That means that at the low notes, the speaker will convert 99% of the electrical energy put into it into heat rather than 95% (numbers pulled completely out of the hat, but speaker efficiencies are indeed rather low). Which will prompt the player to ramp the volume up. So once you are at comfortable, clean playing volume without getting into distortion, the cabinet and speaker bearings get more of a workout than they are used to, and the speaker may, without proper acoustical resistance, hit its linear maximum and/or overheat.
All of the problems have nothing to do with the preamp, and very little with the amp. It's really a speaker/cabinet problem.
So no, this won't help.
@user36187 is right – a preamp will not change anything about the suitability of a guitar amp for amplifying bass. In fact, it would rather exacerbate the problems!
Such preamps are designed to add a bit of colour and possibly distortion to the bass sound. This can make sense if you're plugged straight into a PA or an active monitor speaker, which can otherwise sound dull and/or clinical.
OTOH, a guitar amp has already too much such nonlinearities, that's really the reason why it's not so suited for bass. The response curves of preamp and guitar amp may in some small domain cancel to give an overall better result, but in most of the spectrum they will generally add up to something even more nonlinear.
So, forget about the preamp.
That said... you can play bass straight over a guitar amp. And it will in most cases not fry the speakers – modern guitar amps and cabinets are basically designed to be abused with all kinds of overdriven signals, including low-frequency drops. The problem is more that they handle these signals by ruthlessly decimating/clipping the parts that can't be properly reproduced. That's usually ok for guitar, but for bass you really can't use an uneven LF curve with strange distorted resonances. I also don't much like the transient smoothing that guitar amps tend to cause.
Still – many guitar amps actually give a perfectly usable sound when playing bass over them, especially when you're into more of a dirty sound with a lot of overdriven midrange. In fact many great bassists used guitar amps, either alone (early The Who – John Entwistle would crank up Marshall Stacks) or together with proper bass amps / DI (Chris Squire would split out the signals of his pickups; neck pickup to a mostly clean bass amp and bridge pickup to a distorted guitar amp).
Just when you want a straight / clean / round / funky / modern bass sound, guitar amps are not so great. But I wouldn't hesitate to just give it a try. If you're afraid to damage the speakers, just keep the master volume down a bit.
If you cant get the amp to sound as clear/fat as you need, consider plugging straight into a PA. This again can give perfectly satisfying results. It just depends on what sound you want.
The problem here is that connecting a bass to a guitar amp isn't just about the electrical impedance but also the acoustic properties of a speaker. For obvious reasons a bass generates much lower frequencies than a guitar and lower frequencies are associated with significantly more mechanical power so there is a potential risk that you will physically damage the speaker by trying to drive it at frequencies it is not designed for.
Even if it doesn't do any damage the chances are that it won't sound that great.
It depends a bit on the gear in question as well, a chunky 4x12 cabinet will cope better than a small practice amp but even so bass and guitar speakers and amps are fundamentally different things.
There has been a trend in recent years for bass cabs to get much more compact, or indeed to eliminate them altogether and just go to a PA via a preamp and/or speaker modeller
What is the sound you are out for? A funky, twangy sound, possibly with some level of distortion? Most of the sound energy will likely be in the range a guitar amp is comfortable with. A deep rumble shaking the listeners? The kind of stuff one uses subwoofers and long organ pipes for? That's not the department of a guitar amp, and when you try taking it there, the speaker will throw in the towel quite earlier in comparison to its maximum rating than a bass cabinet would.
In short: the more you want to feel rather than hear your bass, the more of a mismatch a guitar amp may turn out to be. More so if the amp is a small one. Many smaller cabinets are open or semi-open in the back which makes sort of an acoustical short-circuit for notes lower than the ones the cabinet has been designed for. Turning the volume/bass up to compensate will take the amp closer to its limits earlier.
I am fairly certain that the first answer is wrong. Bass will obviously sound better through a bass amp capable of produce low frequencies, but, if you read this: Bass effects through guitar amp answer, it seems like there really is no big problem with playing bass through guitar amps and that it is an "urban legend." I have played bass through guitar amps (at fairly high volumes) and they have not spontaneously combusted. You really should be fine, but, bass amps sound better if you don't want distortion.
I think electronic bass guitar already has an inbuilt pre amp. That is why you can adjust the volume. So adding an external preamp on a guitar amp would not go well. I usually use preamp when I'm connecting directly to mixer just to boost my overall output volume