113 Math
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

  • Logarithm Fundamentals
  • math