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.

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.

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.

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?

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.

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

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.

Change of Base To calculate logs with other bases or

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

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?

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