Solve Exponential and Logarithmic Equations

Lesson 7.6Algebra II

Agenda

Schedule for this week:Monday – lesson 7.6Tuesday – chapter review Wednesday/Thursday – 30 minute review

and Chapter 7 test (7.7 not on test)Friday – Review of 1-14 on handout

Today- Lesson 7.6Homework: 7.6 from the assignment sheet

No Books out please… please take notes.

Solve Exponential and Logarithmic Equations

Let’s say that we would like to solve the following equation:

What would your first step be? Tell your neighbor… when you think you know put your thumb up.

Solve Exponential and Logarithmic Equations

The first step is to get the equations into the same base…

There are a couple of ways to do this…

Solve Exponential and Logarithmic Equations

Could you rewrite 4 and using the base of 2?

Solve Exponential and Logarithmic Equations

Could you rewrite 4 using a base of ?

Solve Exponential and Logarithmic Equations

Either technique will work… let’s see why…

Property of Equality for Exponential Equations:

Algebra: If b is a positive number other than 1, then then

So…

Solve Exponential and Logarithmic Equations

Starting with if and we can substitute both into the equation... using our properties we can say that… (remember the distributive property). From here we can say that

Solve Exponential and Logarithmic Equations

and

Solve Exponential and Logarithmic Equations

Check your answer:Original equation We found that Substitute it back into the equation

Solve Exponential and Logarithmic Equations

original equation and express numbers in same base substitute into equation power of a power property

property of equality for exp eq’nadd x to both sidesdivide both sides by 3

Solve Exponential and Logarithmic Equations

1. original equation 2. express numbers in same base3. substitute into equation4. Use properties of exponents 5. property of equality for exponential equations6. Solve for x7. Check your answer

Solve Exponential and Logarithmic Equations

Do these practice problems:

Solve Exponential and Logarithmic Equations

Sometimes it’s difficult to express things in the same base… for instance.. What would you do if you needed to solve the following equation…

How could you start this problem?

Solve Exponential and Logarithmic Equations

How could you start this problem? Take the log of both sides:

Simplify using the Power property:

Solve for x: Check your answer

Solve Exponential and Logarithmic Equations

Solve Exponential and Logarithmic Equations

1. Take the log of both sides2. Simplify using the properties of logs3. Use algebra to solve for x4. Check your answer

Solve Exponential and Logarithmic Equations

Try these problems:

Solve Exponential and Logarithmic Equations

Property of Equality for Logarithmic Equations:If b, x and y are positive numbers and then if and only if

Example:

Solve Exponential and Logarithmic Equations

Sometimes the easiest way to solve something is by exponentiation…

For instance:

Always check your answers… check for extraneous roots.

Solve Exponential and Logarithmic Equations

Let’s try these problems….