### GIGAMIND

Folder:

113 Math

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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