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Function Notation with Logs and Exponentials  Concept
Carl Horowitz
Carl Horowitz
University of Michigan
Runs his own tutoring company
Carl taught upperlevel math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!
If we want to solve for or describe a region in a coordinate plane, we can use linear inequalities. Linear inequalities give us a set of solutions as opposed to just one solution. Solving linear inequalities uses similar methods as solving multistep equations, except that there are extra rules when using multiplication and division. We graph linear inequalities by shading regions of number lines or coordinate planes.
So we know function notation is basically when you see f of something or g of something and it means to plug in whatever is in the parentheses into your equation. With logarithms it's no different, okay? So behind me I have a simple logarithmic equation, f of x is equal to log base 4 of x qand we're looking it to find f of 16.
The premise is exactly the same, plug in 16. So log base 4 of 16. So now we need to figure out what this is equal to, okay? So couple of ways that you can do that. You can say that this is equal to x put it in exponential form 16=4 to the x. You could change 16 to be 4 squared but hopefully you can recognize this is just going to end up being x=2 so 2 is our answer. Remember we plugged in x to be our our term we don't actually want it to be in our answer.
Another way is hopefully as you see logs a little bit more is you're getting more and more comfortable with how they work, and basically what this is saying is 4 to what power will give us 16, okay? By rewriting that we're saying here. So hopefully by looking you'll get into a point where you're looking at these and you're saying,okay. 4 to what power gives me 16, 4 squared so then my answer is 2.
So solving the a logarithmic equation in function notation, the same exact thing as you would any log equation or anything in function notation. Just the two of them put together.
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Carl Horowitz
B.S. in Mathematics University of Michigan
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Sample Problems (3)
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Function Notation with Logs and Exponentials
Problem 1 5,916 viewsg(x) = 3[log_{3}(5x − 1)]² + 1
g(2) = 
Function Notation with Logs and Exponentials
Problem 2 5,482 viewsAmount of radioactive material decays such that the amount remaining after time, t, is given by f(t) = 100 ⋅ 2^{t} grams.
a) initial amount of materialb) amount after 4 years?c) When will there be 50 grams left? 
Function Notation with Logs and Exponentials
Problem 3 1,431 views
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