The logarithm relationship to powers and squares

In math there is a beautiful relationship between powers, squares, and logarithms.

Think about the following

\(10^3 = 1,000\) \(\sqrt[3](1,000) = 10\) \(\log_{10}(1,000) = 3\)

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:

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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