A Scottish mathematician named John Napier discovered logarithms in the early 17th century & the world has never been the same since.
The pH scale in chemistry is logarithmic as is the well-known Richter scale used to measure seismic interest. The basis for any logarithmic scale is that an increase in one unit means a tscheme increase that is tenfold. For example, a Richter 7 earthquake is 10 times as strong as a Richter 6 & 100 times stronger than a Richter 5 quake. The measurement of sound in decibels (dB) is one more locale where logarithms are used. Total silence is 0 dB, a guy breathing is 10 dB, & a loud rock concert is about 120 dB. A quiet library comes in at about 40 dB so it is no surprise that an outdoor AC compressor making a 60 dB sound will acquire a stern look from the librarian. Many factors affect the sound that Heating, Ventilation, & A/C units make. A solidly built one will be quieter than a flimsy model. Heating, Ventilation, & A/C units get louder as they age, then larger capacity units will produce a louder sound & if you allowed your unemschemed aunt to install it imrespectfully, you may have lost sleep when the unit begins to rattle at 2:00 a.m. when even your youngsters are quiet. Manufacturers are aware that people want & need a quiet environment & have come up with innovations like variable-speed blowers, sound dampening outdoor cottageets, quieter fans, & even discharge mufflers. If your aunt installed that Heating, Ventilation, & A/C condenser right outside your study room window, you may want to call a qualified Heating, Ventilation, & A/C company to see if it can be moved to a location where the noise won’t keep you awake at evening.