Logarithms. Why? How? Who Cares? Picture of a crab saying, let's say I'm just walking along one day... and a fish saying, Dennis, how many times do I have to multiply 8 by itself to get 218614? gif of crab eyes going back and forth octopus asks crab, Yeah, Dennis can you solve 8 to the x equals 218614? crab says, Looks like we need to find an exponent. we can try... flashing gif that says Ye Olde Guess and Check 8 to the question mark equals 218614
8
=
crab says it's between 5 and 6. Octopus says Dennis I need an exact value. Fish says, Tedious, Dennis. This is urgent.
Crab says, Well Folks, the exponent you're looking for is Log base 8 of 218614 sound on
gif of octopus inking saying, Too Scary Crab holding a calculator says When I plug it into my calculator, I get 5.9127 gif of exponential equation where the exponent alters between Log base 8 of 218614 and 5.9127 Logs are numbers! They're the exponents! Octopus says Help me find that exponent and crab says, this log will help hahah Any time the variable is in the exponent, use a log. Crab says, we can rewrite any exponent equation as a log equation. 4 to the x equals 500 is the same as Log base 4 of 500 equals x.
Log
=
=
crab says This is how we switch between exponential and logarithmic form
gif switching from log to exponential forms sound on
fish says, So what number is log base 6 of 59? Crab replies, No discrimination! Log base 6 of 59 is a number. Fish replies, meh what decimal is it? Crab replies, Oh approximately 2.2757
Crab says, Ok let's do everyone's favorite, A Real Life Example! Octopus says, But this is real life. Math is beautiful for its own sake. Fish says, Woohoo. The example problem is: Our underwater city mayor has decided to defund the police as a step to abolition. The mayor is going to invest the money into our community support systems. The current budget is 588 million. If we defund at 5% per year, when will the budget be $100? sound on
588000000 0.95 to the x 100

This is the starting police budget

This is the percent of the current year's budget we have for the next year. Defunding by 5% means that next year will have 95% of this year's budget.

How many years this will take! This is what we are solving for.

What we want the budget to be! $100 is plenty for the police.

Now we can solve for x. Crab says divide by 588 million. Octopus says, Swoop de loop it. Fish says, use a calculator to get an approximate decimal value. x is equal to 303.88 years. The octopus and fish say, boo too long. The crab says, But yay for logarithms showing us the truth! sound on
Current Police Budget $
Rate of defunding $
%
What do you want their budget to be? $1? The current school budget?
Crab, octopus, and fish are touching each other looking happy