SOLVING LOG EQUATIONS HOW TO SOLVE A

Haberman MTH 111 Section II: Exponential and Logarithmic Functions Unit 6: Solving Exponential Equations and. Recognize that the resulting value. Use the product rule to turn the right side of the equation into a single logarithm. Describe the strategy you would use to solve log 6x log 64+log 68. Square all logarithmic expressions and solve the resulting quadratic equation.

Students come into class with 3 algebraic problems to solve. A2.3.2 Explain and use basic properties of exponential and logarithmic functions and the inverse relationship between them to. Some useful properties are as 9.6 Solving Exponential and Logarithmic Equations. Solve the following: (a) log3 x 4 (b) logm 81 4 (c) logx 1000 3 (d) log2 x 2 5 (e) log3 y 5 (f) log2 4x 5 Section 2 Properties of Logs Logs have some very useful properties which follow from their de nition and the equivalence of the logarithmic form and exponential form. I develop solving equations with these functions by discussing how the process is just like solving any algebraic equation.3.

Solving Log Equations How To Solve A

This problem is easily solved by factoring. Students must rearrange the equation and then remember how to solve a quadratic. Students all know how to solve this so students quickly gain confidence that this lesson is not too hard.The second equation is a quadratic.

The answer here is -12 which will not work for this equation. This problem also reminds students that it is necessary to check their solution to verify the value found fits the domain for each function in the equation. This is a useful property. I identify students who struggle so that I can assist them with solving quadratics later.The last problem show students demonstrates how you can solve when you have f(a)=f(b) Since both sides have a square root the inside functions must be equal. Many students are not proficient with solving equations and try to isolate the x^2 instead of setting the equation to zero.

I expect that some will be unsure how to finish the problem. I will give my students a couple of minutes to work on the first problem. When the type of function changes the domain may change and that is why we get extraneous solutions.I now give students a pair of exponential equationsВ to solve.

Students will solve this problem and share their process with the class. At this point I (or a student) will say, 'What is the inverse of e^x?' Once students remember the inverse is ln x we take the inverse of both sides and find the answer.Additional questions my students often ask:After we discuss the first problem, the students move to the next problem. If so, I'll ask, 'Why square root?' Someone usually identifies this as the inverse operation. Most students will say square root.

As I move around I think out loud to help students think about the problem. We will work one problem at a time. As I progress through the unit I will use solving to show the change of base formula.Today we are again working from exponential to lograithmic, so I will now give students several logarithmic equations to solve. We will then discuss how you need to use the inverse.At this point I have not discussed the change of base formula or how we need to solve using common logarithms or natural logarithms. When this happens I try to showВ the student what they really did. Some students will try to divide by the base.

We discuss how both methods are correct ways to begin the problem and both yield the same answer. Other students take the inverse of each side. One is to see that both logarithms are the same so the arguments have to be equal. I usually have 2 different processes used. I have a student share their process. These are usually the firstВ to find the answer.After 2-3 minutes, I bring the class back together.

Here we have 2 terms on the right. I remind them that this was possible because we have one term on each side of the equation. Some students want to just remove the logarithm off the terms like they did with the first problem. The last problem is the most difficult for the students. I also let students know that I do not usually require using the calculator because I am looking at their process of problem solving.We move on and work each problem. I tell the students that directions for the problem will explain.

Once this is done students are able to solve.

Solving Log Equations Pdf