Name: juan a cornejo
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Question:
What is a natural logarithm? How would I solve one?
High School Calculus Student.

Replies:
Let's talk about square roots first. If you have an equation
X^2 = 4
then X = squareroot(4) = 2
If we have
X^2 = 3.8
then X = squareroot(3.8) which we need a calculator or
slide rule to find a numerical approximation to X (about 1.94936).
Now, to logarithms. If you have an equation
2^X = 4
then X = logbase2(4) = 2
If we have an equation
10^X = 100
then X = logbase10(100) = 2 (because 10^2 = 100).
There is a number called e which, like pi, pops up a lot in
mathematics. The logbasee is called the "natural logarithm."
So, sometimes you have an equation
e^X = 100 to solve.
From a calculator or slide rule, we can figure out that
X = logbasee(100) = 4.60517...
because e, which equals about 2.7182818... to the power 4.60517...
equals 100! (try it on a calculator and see!)
Sometimes the natural logarithm is indicated by ln and the base ten
logarithm by log. so 10^x = 100; x = log(100) = 2;
e^X = 100; X = ln(100) = 4.60517...

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