This manipulative was made in collaboration with Bryan Bazilauskas - a math teacher in the Los Angeles area, thanks Bryan!
We wanted to highlight the relationship between the logarithm and the exponent.
That’s it. That’s a log.
Practically speaking, it’s helpful for manipulating equations that have an exponent. Likewise, exponents are helpful for manipulating equations that have a logarithm. This makes them ‘inverses’ of each other.
To evaluate, ask yourself: “How many instances of the log’s base are there?” To answer that, factorize.
With this fundamental understanding of what a log is, you can derive most of the ‘rules’ that a typical algebra class will ask you to memorize.
Memorizing stuff is tedious and fades away quickly from lack of use. It’s easier in the long run to get a firm grasp of the fundamentals and derive its applications when needed.