# Function Notation with Logs and Exponentials - Concept

###### Explanation

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 multi-step 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.

###### Transcript

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.