why is the natural logarithm (log base) more commonly used than the logarithm base 10 in many areas of science and engineering?
In: Mathematics
There’s a reason it’s called the “natural” logarithm, and that’s because it’s base e and logarithms are related to exponents (the inverse). e is important and “natural” in math because e^x is it’s own derivative, and that’s an EXTREMELY useful fact in much of math. And because logarithms are the inverse to exponents, and e^x is such an important exponent, ln is such an important logarithm.
Note, there’s nothing magical about it, some number HAD to be, it is guaranteed, and e is that number.
Also note that log 10 is still widely used outside of mathematical equations. If you ever see a log-scaled graph and it has units, that’s going to be a log 10, not ln. As important as e is to math, it is extremely inconvenient to present your numerical results in base e rather than base 10, lol.
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