What is a natural logarithm? Why is ln(1) = 0?
In: Mathematics
2 to the power of what makes 16?
2⁴ = 16 so the solution to that question is 4. We write that as log(16) = 4.
3 to the power of what makes 16?
Its a bit more complicated but we also call the number that solves this question log(16). However, the fact that we are taking powers of 3 this time obviously makes this number different to the other “log(16)”. So to resolve that issue, we call this one “log to the base of 3” and the other one “log to the base of 2”. Usually, you just write “log(16)” and add the base as a small subscript.
Now, “log(1) to the base of 2” simply means
2 to the power of what makes 1?
Since everything to the power of 0 is one, we actually know that log(1) = 0 *regardless of base* .
Next, the natural logarithm is just the logarithm where the base is a special number called “e” or eulers constant. Its about 2.71… and due to some calculus reasons, its a very handy base (and in some sense the “natural” choice of base). Still, ln(1) = 0 remains true.
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