In Exercises 14, find vector and parametric equations of the line containing the point and parallel to the vector. Point: ; vector:
Here is the definition of the logarithm function. If b is any number such that and and then, We usually read this as “log base b of x”. In this definition is called the logarithm form and is called the exponential form. Note that the requirement that is really a result of the fact that we are also requiring . If you think about it, it will make sense. We are raising a positive number to an exponent and so there is no way that the result can possibly be anything other than another positive number. It is very important to remember that we can’t take the logarithm of zero or a negative number. Now, let’s address the notation used here as that is usually the biggest hurdle that students need to overcome before starting to understand logarithms. First, the “log” part of the function is simply three letters that are used to denote the fact that we are dealing with a logarithm. They are not variables and they aren’t signifying multiplication. They are just there to tell us we are dealing with a logarithm. Next, the b that is subscripted on the “log” part is there to tell us what the base is as this is an important piece of information. Also, despite what it might look like there is no exponentiation in the logarithm form above. It might look like we’ve got in that form, but it isn’t. It just looks like that might be what’s happening. It is important to keep the notation with
