# Logarithmic relationship definition dictionary

### logarithmic - Dictionary Definition : omarcafini.info

In mathematics, the logarithm is the inverse function to exponentiation. That means the More explicitly, the defining relation between exponentiation and logarithm is: log b (x) = y {\displaystyle \log _{b}(x)=y\quad Logarithmic function[edit]. To justify the definition of logarithms, it is necessary to show that the equation. At another point, Judge Alsup and Allen went on a long, wandering detour about whether the relationship between two variables was logarithmic or linear. Comprehensive list of synonyms for general words relating to mathematics and geometry, by Macmillan Dictionary and Thesaurus.

Hopefully these examples have given you a better feel for what a function actually is. We now need to move onto something called function notation.

### logarithm | Definition of logarithm in English by Oxford Dictionaries

Function notation will be used heavily throughout most of the remaining chapters in this course and so it is important to understand it. The letter in the parenthesis must match the variable used on the right side of the equal sign. If you keep that in mind you may find that dealing with function notation becomes a little easier.

This is one of the more common mistakes people make when they first deal with functions. This is just a notation used to denote functions.

Next we need to talk about evaluating functions.

Evaluation is really quite simple. So, when there is something other than the variable inside the parenthesis we are really asking what the value of the function is for that particular quantity.

The key here is to notice the letter that is in front of the parenthesis.

## logarithmic scale

In other words, we just need to make sure that the variables match up. Here are the evaluations for this part.

**Comparing exponential and logarithmic functions - Algebra II - Khan Academy**

Here are the evaluations. Now the second one. Recall that when we first started talking about the definition of functions we stated that we were only going to deal with real numbers. In other words, we only plug in real numbers and we only want real numbers back out as answers.

Based only on these three points, plot the three corresponding points that must be on the graph of y is equal to log base b of x by clicking on the graph. I've actually copy and pasted this problem on my little scratch pad so I can mark it up a little bit.

## 1. Definitions: Exponential and Logarithmic Functions

What is this first function? This first function is telling us so x, and this is y is equal to b to the x power. When x is equal to zero, y is equal to one.

That's this point right over here. When x is equal to one, b to the one power or b to the first power is equal to four.

- Relationship between exponentials & logarithms: graphs

Another way of thinking of this y or four is equal to b to the first power and actually we can do [said] must be four. That's this point right over there. This point is telling us that b to the second power is equal to When x is equal to two, b to the second power, y is equal to Now we want to plot the three corresponding points on this function.

### Logarithm - Wikipedia

Let me draw another table here. Now it's essentially the inverse function where this is going to be x and we want to calculate y is equal to log base b of x.

What are the possibilities here? What I want to do is think Let's take these values because these are essentially inverse functions log is the inverse of exponents. If we take the points one, four, and What is y going to be here? This is saying what power I need to raise b to to get to one. If we assume that b is non zero and that's a reasonable assumption because b to different powers are non zero, this is going to be zero for any non zero b.

This is going to be zero right there, over here. We have the point one comma zero, so it's that point over there.