What Is a Field? What Are Instants and Durations? A duration is a measure of elapsed time. It is a number with temporal units such as years or seconds.

However, if we put a logarithm there we also must put a logarithm in front of the right side. This is commonly referred to as taking the logarithm of both sides.

This is easier than it looks. It works in exactly the same manner here. Both ln7 and ln9 are just numbers.

Admittedly, it would take a calculator to determine just what those numbers are, but they are numbers and so we can do the same thing here. Also, be careful here to not make the following mistake. We can use either logarithm, although there are times when it is more convenient to use one over the other.

There are two reasons for this.

So, the first step is to move on of the terms to the other side of the equal sign, then we will take the logarithm of both sides using the natural logarithm.

Again, the ln2 and ln3 are just numbers and so the process is exactly the same. The answer will be messier than this equation, but the process is identical.

Here is the work for this one. That is because we want to use the following property with this one. Here is the work for this equation. In order to take the logarithm of both sides we need to have the exponential on one side by itself.For example, the area of a rectangle is length times width.

Well, not every rectangle is going to have the same length and width, so we can use an algebraic expression with variables to represent the area and then plug in the appropriate numbers to evaluate it.

To review how to obtain equations from linear graphs, see Obtaining the Equations of a Line, and from quadratics, see Finding a Quadratic Equation from Points or a Graph..

Here are the graphs, with explanations on how to derive their piecewise equations: Absolute Value as a Piecewise Function. In this section we solve linear first order differential equations, i.e. differential equations in the form y' + p(t) y = g(t).

We give an in depth overview of the process used to solve this type of differential equation as well as a derivation of the formula needed for the integrating factor used in the solution process. Nov 09, · Find out how to write the equation of an absolute value function given only its graph.

Question Write an absolute value equation that has 5 and 15 as its solution. what I've tried: 5|x+2|=15 and it was a "no solution" all my equations that I try come out with a "no solution" meaning that the absolute value was a negative number.

Perform inverse operations until the absolute value stands by itself on one side of the equation--the equation should be of the form|expression| = c. If c is negative, the equation has no solution. Separate into two equations: expression = c or expression = -c.

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