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Warm Up

Warm Up. Solve the following without graphing. x =3 x =2.5 x =-3 x =3 Cant be done…. Investigation. What is the exponent? 10 x = 1 10 x = 10 10 x = 100 10 x = 1000 10 x = 10000 The log button on the calculator is log base 10. Calculate the following Log 1 Log 10 Log 100

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Warm Up

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  1. Warm Up • Solve the following without graphing. x =3 x =2.5 x =-3 x =3 Cant be done…

  2. Investigation • What is the exponent? • 10x = 1 • 10x = 10 • 10x = 100 • 10x = 1000 • 10x = 10000 • The log button on the calculator is log base 10. • Calculate the following • Log 1 • Log 10 • Log 100 • Log 1000 • Log 10000 • What is the exponent? • 2x= 1 • 2x= 4 • 2x= 8 • 2x= 16 • 2x= 32 • Graph y = log2x and fill in the table.

  3. 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?

  4. Logarithims • 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.

  5. Natural log and Common Log • Common Log • Base 10 • The log button • Not written • Natural log • Base e • Growth/decay rate • What have you talked about in science?

  6. Change of Base • To calculate logs with other bases • or

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

  8. 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?

  9. 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 loge e

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