I need some help understanding how logarithms work. I just can’t wrap my head around the concept, and I can only find videos online explaining how to rearrange a log equation. I’m looking for an explanation as to how it works, and perhaps the theory behind it.
I’ve also heard that log is easier to use for more complex calculations. How does rounding work with log? What is a natural log? What is e?
In: 3
A logarithm is the opposite of an exponent. If Log^(a)(b) = c, that is equivalent to saying that a^c = b.
What really helped it click for me is this: If you take any given number X, calculate the base 10 logarithm, and round up, you will get how many digits long X is.
This is because any one-digit number is between one (10^(0)) and ten (10^(1)), any two-digit number is between 10^1 and 10^(2), any three-digit number is between 10^2 and 10^(3), etc.
e (AKA Euler’s number) is a special constant value that comes up a lot when dealing with exponents. It’s sort of like how pi is equal to 3.14… but e is approximately 2.718. One property of this number is that if you graph f(x) = e^(x), the value of the function at any given point is also equal to the slope of the function at that point, and its the only function with that property.
The natural logarithm (usually written “Ln” but sometimes just “Log”) is just a logarithm of base e. So just like above, Ln(a) = b is the same as saying a = e^(b).
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