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….
Top Related