1. Evaluate the expressions: log 3 27log 2 ½ log 25 5 2. Sketch the graph of f(x) = 4 x and tell the domain, range, intercept, asymptote, and end behavior.

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Presentation transcript:

1. Evaluate the expressions: log 3 27log 2 ½ log Sketch the graph of f(x) = 4 x and tell the domain, range, intercept, asymptote, and end behavior. 3. Sketch the graph of log 4 x and tell the domain, range, intercept, asymptote, and end behavior.

 By the end of today, you will be able to… ◦ Understand and use the properties of logarithms ◦ Understand and use the change of base theorem

 They are just like the laws of exponents.  Why does this make sense?

 log b 1 =  log b b =  log b b x = What about ln? ln e = Log10 =

 log b xy = log b x + log b y  What exponential rule does this remind you of?  Example: log 3 54

 Example: log 9 36

 Examples: log 4 x 9 5 ln e 2 – ln e 3 Evaluate this expression

 This allows us to use our calculator to estimate log values that have bases other than 10 or e. (ln)  Our calculator only has the two common log buttons.

 Evaluate each logarithm: log 3 5log 1/2 6

 Rewrite the following expression using the product property:log20  Rewrite the following expression using the quotient property: log40  Rewrite the following expression using the power property: 3log10

 They help us manipulate, evaluate, simplify, expand, and condense logarithmic expressions however we’d like to.  And ultimately, they help us solve equations with exponents and logarithms.

Asks us to:  Make all coefficients exponents  Rewrite the expression using only 1 log

 Condense this expression: 4logx – 3log5x  Condense this expression: 6 ln(x – 4) + 3 lnx

Asks us to…  Rewrite the expression using MORE THAN 1 log  Make all exponents coefficients

 Expand this expression: log12x 5 y -2  Expand this expression:

The power property lets us get variables out of the exponent!  Remember our problem from Friday? 300 = 200e.05t 4 x+ 2 = 10

 Complete the problems on the back of your guided notes sheet for today.  Working diligently earns you your class work stamp!  Whatever you do not finish in class is your homework.  p. 185 # 19 – 24, 29 – 32, 39 – 44, 49 – 58, p. 186 #

 Study for your quiz Wednesday (exponential word problems, graphs of exponential functions and logarithms)  Complete problems 21, 25, 37, 40 on the back of your notes from Thursday, as well as any other problems you did not finish today in class.

 You have today, tomorrow, Thursday, and Friday afternoons to make test corrections if you would like to.  If you would like to know your current grade in the class, or have other questions, come see me after school!