**Logarithmic functions** are those that have certain definite, fixed exponents, such as: e, F, T, Sine, andsin, to mention a few. By understanding how these exponents change as the values alter, you can understand why they tend to give different answers to the same question, for instance: “What is the value of x at x + t.” The function whose answer you want to get is called, in layman’s terms, logarithmic. The range of values it will accept varies from function to function. In general, however, the range of values that you can expect from any logarithmic function is just a finite number such as:

We now know what causes the end behavior of these parent functions. We see that it varies according to the order of integration, i.e., (i.e., higher order integration produces lower bounds and higher bounds produce lower bounds). It also varies according to the value of the integral, which we saw above. Finally, it varies according to the interval size that the function is defined by.

In the previous lesson, we saw how to solve for the normal curve. Let us see how to solve for the exponential function, which is the most commonly used log-log function. The first step is to set up a table showing all of the inputs that the function takes as it varies through time. This is called the integral domain, and the interval domain is the space that separates the points on the interval from zero on one end of the function to infinity on the other end. Next, set up another table showing all of the outputs of the function at different times, called the Taylor series.

Here is one more important point about the Taylor series: many students find that they cannot solve it using the asymptotes in the pre-calculus example. They find that there are not enough values left in unit 1 to allow them to complete the function on the end of the interval. As a result, they move on to units that contain smaller values of the integral. In this lesson, you will learn about how to handle these asymptotes so that you can use them correctly in your problems.

Here is a quick tip for the **end behavior of logarithmic functions** when they are graphed using the binomial tree. The binomial tree shows how the logarithmic functions form a power series, with each leaf representing a distinct range of the natural logarithmic. So, if we plotted the logarithmic functions on the chart, we would see a familiar tree design. Notice that as we move from left to right along the chart, the height of the branches get smaller.

This tip gives us one more way to understand the** end behavior of logarithmic functions** better. Let us say that we plotted the logarithmic function on a vertical axis. We could see that the height of the branches gets smaller as we move away from the origin. To plot the function on a horizontal axis, we would have to add some horizontal bars to indicate the range of the natural logarithmia. Now that we understand the end behavior of logarithmic functions using this information, we can apply it to solve more difficult problems in higher mathematics, such as those involving elliptic equations.

## How to Use a Logarithmic Function

Logarithmic functions are those of the inverse transformations of arithmetically exponential functions. While working with numbers of an even smaller size, logarithmic functions take a finite amount of time to reach the results, since they can be decomposed into the original form more quickly. In other words, a number n can be represented as being approximately represented by n-log(n). This form is also known as the logarithmic function. Logarithmic values were discovered by Sir William Taylor along with others following a period of experimentation in mathematics.

The logarithmic functions satisfy certain essential criteria, such as exponents of logarithmically natural numbers and the equality (or inequality) of their successive values. Let’s say, for example, that we have a number of which has been increasing in value for some time, and we will use this value to define a new number, y, equal to (x-1) where x is prime. According to logarithmic functions, if we take the first term, log(x), and add the second term log(y), we get the third term, which is also a positive number, therefore, we have the expression, log(x) log(y).

A logarithmic function can also be graphed, as a function of some real number y whose starting value is x. It is a very convenient graph because it enables one to plot a waveform of the exponential equation, as it were. It can also be plotted as a function of some real number x whose starting value is zero. Such graphs are called a logarithmic function graphed in the plane, or cubic bode function, since they are plotted as a function of some real number, which can be plotted on any graph.