1. Warm Up Solve the following without graphing. x =3 x =2.5 x =-3
Cant be done…
1 – 4 students can do w/o a calculator. Problem 5 can not. That should lead to a discussion of what logs are, and how they are used to solve for the missing exponent.

2. Investigation What is the exponent? Calculate the following
The log button on the calculator is log base 10.
Calculate the following
Log 1
Log 10
Log 100
Log 1000
Log 10000
Students will need instructions on how to enter logs w/ base other than 10 into the calculator.

3. Investigation What is the exponent?
Graph y = log2x and fill in the table. x y 1 2 8 16 32
Students will need instructions on how to enter logs w/ base other than 10 into the calculator.

4. Investigation
Compare the exponential equations with base 10 to the log equations. What do you notice?
Does the same thing appear to happen with the base 2 equations?
How are the exponentials and logs related?

5. Logarithms Logs = exponents
Used to solve when the variable is in the exponent.
Logs and Exponentials are inverses (undo) of each other.
Examples: Rewrite each of the following.

6. Common Log Common Log Base 10 The log button Not written
In science they have talked about half life, and bacteria growth.

7. Natural log Natural log Base e Growth/decay rate
What have you talked about in science?
In science they have talked about half life, and bacteria growth.

8. Change of Base
To calculate logs with other bases or

9. Solving with Logs Rewrite as a logarithm and solve.
Plug solution back into the original equation to check.

10. Solving with Logs
A bank is offering a CD with 3.25% interest compounded continuously. How long will it take your investment to double?
The half-life of a radio-active material is 245 years. What is the rate of decay?

11. Summary Logs = _________
To solve when x is in the exponent, _____________
logA has a base of ___ and can be rewritten _________
lnA has a base of ___ and can be rewritten ________
Solve these problems on your post-it note and turn in.
Exponents
rewrite as a log 10
log10 e
loge