Why is the decibel scale logarithmic?

Human senses, nearly all, work in a manner and obey Weber–Fetcher law, that response of the sense machinery is logarithm of an input. It is true at least for hearing, but also for eye sensitivity, temperature sense etc. And of course, in areas where it works normally. Because in extreme, there are other processes such as pain, etc.

So as in a cause of hearing, what you experience is the logarithm of power of a sound wave, by "biological, natural, hear sense construction. So, it is natural to use logarithmic units.

I don't know anything about the history of the Bel and related measures.

Logarithmic scales--whether for audio intensities, Earthquake energies, astronomical brightnesses, etc--have two advantages:

• You can look at phenomena over a wide ranges of scales with numbers that remain conveniently human-sized all the time. An earthquake you can barely detect and one that causes a regional disaster both fit between 1 and 10. Likewise the stillness of an audio-dead room and the pain of an amp turned up to 11 fit between 10 and 130.
• Fractional measures are converted into differences which most people find easier to compute quickly. Three decibels reduction is always the same fractional difference; the EEs get a lot of mileage out of this.

These scales may seem very artificial at first, but if you use them they will become second nature.

It's just because sounds that the human ear is capable of hearing range over a very large range of amplitudes. If you talked about the power delivered to the ear, rather than the log of the power delivered to the ear, you would need to use numbers like $10^{12}$ to talk about airplane engines. So, rather than deal with that, we use logarithims, so that most of the numbers we deal with when talking about sounds vary over reasonable number ranges.