# Rewrite as a single logarithm and simplify your life

Due to the nature of the mathematics on this site it is best views in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device should be able to scroll to see them and some of the menu items will be cut off due to the narrow screen width. First plug the sum into the definition of the derivative and rewrite the numerator a little. Due to the nature of the mathematics on this site it is best views in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device should be able to scroll to see them and some of the menu items will be cut off due to the narrow screen width.

Linear Differential Equations The first special case of first order differential equations that we will look at is the linear first order differential equation. In this case, unlike most of the first order cases that we will look at, we can actually derive a formula for the general solution.

The general solution is derived below. However, we would suggest that you do not memorize the formula itself. Instead of memorizing the formula you should memorize and understand the process that I'm going to use to derive the formula. Most problems are actually easier to work by using the process instead of using the formula.

So, let's see how to solve a linear first order differential equation. It's sometimes easy to lose sight of the goal as we go through this process for the first time. In order to solve a linear first order differential equation we MUST start with the differential equation in the form shown below.

In other words, a function is continuous if there are no holes or breaks in it. Do not, at this point, worry about what this function is or where it came from. We can now do something about that. All we need to do is integrate both sides then use a little algebra and we'll have the solution. It is vitally important that this be included. If it is left out you will get the wrong answer every time.

This will NOT affect the final answer for the solution.

So with this change we have. There is a lot of playing fast and loose with constants of integration in this section, so you will need to get used to it. When we do this we will always to try to make it very clear what is going on and try to justify why we did what we did.

This is actually an easier process than you might think. So, to avoid confusion we used different letters to represent the fact that they will, in all probability, have different values. This will give us the following. We do have a problem however. This is actually quite easy to do.

We will not use this formula in any of out examples.Your expression has two logarithms and the problem is to rewrite this as a single logarithm. Somehow we must find a way to condense/combine the two logs into one. There are two ways to combine logarithmic terms: Add or subtract them. As usual, however, the terms must be like terms.

Like logarithmic terms have the same bases . But there are properties of logarithms which allow us to combine these logarithms into one: With these properties all you need is the same base and coefficients of 1 and your logarithms meet both requirements.

You can put this solution on YOUR website! The "^" symbol is used to represent exponents -- not to indicate the base of a logarithm.

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Your question is Given that and then show that It looks ugly (especially the way you showed it!), but everything falls in place nicely using basic rules of logarithms. High School Math Solutions – Logarithmic Equation Calculator Logarithmic equations are equations involving logarithms. In this segment we will cover equations with logarithms.

Nov 10,  · Add logs = multiply It follows that multiplying a log raises to a power. log p + log p = p*p 2*log p = p^2 Subtract logs = divide With those rules in mind, and noting that all your logs are to the same base (which makes life easier): Status: Resolved.

Rewrite the expression as a single logarithm and simplify the result. ln lcosxl +lnltanxl.

Logarithm Expression: How to rewrite logarithm equation as an exponential equation | Math Warehouse