Folder:
113 Math
File:
113.021.01 Logarithms - relationship to powers and squares
The logarithm relationship to powers and squares
In math there is a beautiful relationship between powers, squares, and logarithms.
Think about the following
$$10^3 = 1,000$$
$$\sqrt3 = 10$$
$$\log_{10}(1,000) = 3$$
It's like a triangle. You are given values on two of the points and need to figure out the third. In the first formula you are given 10
and 3
and come up with 1,000
.
Here's a great screen cap from the video source:
The log
wants to be an exponent! It wants to be the exponent of whatever number you're trying to get the log of. E.g. log(100) = 2
--> the log wants to be whatever exponent of 10
that equals 100
.
- IF the log is a different base, you are just trying to figure out what the exponent of the given base is in order to get the number in the parens. E.g. log_3(9) = 2
Source:
- Logarithm Fundamentals https://www.youtube.com/watch?v=cEvgcoyZvB4
Tags:
- math
Graph:
- 113.021.01 Logarithms - relationship to powers and squares >> 113.021 Logarithms
- 113.021.01 Logarithms - relationship to powers and squares >> 113 Math
- 113.021 Logarithms >> 113.021.01 Logarithms - relationship to powers and squares