Thanks to Napier's endeavor, he could substantially reduce his workload, which previously demanded close to a thousand pages of computations, allowing him to devote more time to philosophical speculations. Johannes Kepler, at the time working on his famous laws of planetary motions, was among them. As a result, many astronomers were struggling with endless calculations to detect the position of the planets using Copernicus's theory of the solar system. Napier's scientific activities coincided with the era of new developments in astrophysics. The new computational procedure was instrumental in the field of astronomy. The below table represents some frequent number common and natural logarithms. Logarithm tables that aimed at easing computation in the olden times usually presented common logarithms, too. It is used, for example, in our decibel calculator. It is also known as the decimal logarithm, the decadic logarithm, the standard logarithm, or the Briggsian logarithm, named after Henry Briggs, an English mathematician who developed its use.Īs its name suggests, it is the most frequently used form of logarithm. The other popular form of logarithm is the common logarithm with the base of 10, log₁₀x, which is conventionally denoted as lg(x). Two common variables involve natural logarithm: the GDP growth rate and the price elasticity of demand. Since growth rates often follow a similar pattern as the above example, economics also heavily rely on natural logarithms. Instead, it becomes somewhat stable: it's approaching a unique value already mentioned above, e ≈ 2.718281. You may notice that even though the frequency of compounding reaches an unusually high number, the value of (1 + r/m)ᵐ (which is the multiplier of your initial deposit) doesn't increase very much. Now let's check how the growing frequency affects your initial money: Now, let's imagine that your money is recalculated every minute or second: the m became a considerably high number. It is easy to see how quickly the value of m is increasing if you compare yearly (m=1), monthly (m=12), daily (m=365), or hourly (m=8,760) frequencies. Let's assume that you deposit some money for a year in a bank where compounding frequently occurs, thus m equal to a large number.
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