1. Logarithmic Functions
Objectives: Students will be able to…
Convert between exponential and logarithmic equations
Evaluate logarithmic equations
Graphing logarithmic functions
Domain of logarithmic equations
Solving logarithmic equations
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2. Essential Questions
How are exponential and logarithmic functions related?
How do you convert logarithmic functions to exponential functions? Exponential to logarithmic?
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3. Logarithmic Functions Shortcuts
log10 x = log x (Common log)
loge x = ln x (Natural log)
where e = (Euler’s number – irrational)
logb1 = 0 (because b0 = 1)
logbb = 1 (because b1 = b)
logbbr = r (because br = br)
blog b M = M (because logbM = logbM)
Simpify.

4. Base Solution Exponent
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6. logBASEANSWER=EXPONENT
Objective: Students will be able to convert between logarithmic and exponential functions
CCSS: F-BF.4 Inverse functions, F-LE.4 Logarithmic functions
Essential Question: What strategies do you use to solve logarithmic equations?
Converting
BASEEXPONENT = ANSWER
42 = 16
4 is the base. 2 is the exponent. 16 is the answer.
logBASEANSWER=EXPONENT
log 4 16 = 2

7. b = ln 9
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8. ln b = - 3
ln b = - 3
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10. Evaluating Logarithmic Functions
Objective: Students will be able to convert between logarithmic and exponential functions
CCSS: F-BF.4 Inverse functions, F-LE.4 Logarithmic functions
Essential Question: What strategies do you use to solve logarithmic equations?
Evaluating Logarithmic Functions
1. log
3. log
Base other than 10
Calculator: Math > logBASE()

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12. Graphing Logarithmic Functions
Objective: Students will be able to convert between logarithmic and exponential functions
CCSS: F-BF.4 Inverse functions, F-LE.4 Logarithmic functions
Essential Question: What strategies do you use to solve logarithmic equations?
Graphing Logarithmic Functions
1) y = log x 2) y = 2log (x+3) – )

13. Properties of Logarithms
Objective: Students will be able to convert between logarithmic and exponential functions
CCSS: F-BF.4 Inverse functions, F-LE.4 Logarithmic functions
Essential Question: What strategies do you use to solve logarithmic equations?
Properties of Logarithms
logbM + logbN = logb(MN)
Ex: log4(5·3)
logbM – logbN = logb(M/N)
Ex: log3(50/2)
r logbM = logbMr
Ex: log7 x3
logbM-1 = logb(1/M)
Ex: log11 (1/8)

14. Simplify log 7 + log 4 – log 2 = Simplify ln e2 =
Objective: Students will be able to convert between logarithmic and exponential functions
CCSS: F-BF.4 Inverse functions, F-LE.4 Logarithmic functions
Essential Question: What strategies do you use to solve logarithmic equations?
Worktime
Simplify log 7 + log 4 – log 2 =
Simplify ln e2 =
Simplify e 4ln(3) - 3ln(4) =
Expand log =
Expand ln (abc) =

15. Simplify log 7 + log 4 – log 2 = Simplify ln e2 =
Objective: Students will be able to convert between logarithmic and exponential functions
CCSS: F-BF.4 Inverse functions, F-LE.4 Logarithmic functions
Essential Question: What strategies do you use to solve logarithmic equations?
Worktime
Simplify log 7 + log 4 – log 2 =
Simplify ln e2 =
Simplify e 4ln(3) - 3ln(4) =
Expand log =
Expand ln (abc) =

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17. Inequality Set Notation
Objective: Students will be able to convert quadratic equations.
CCSS: A-REI.4 Re-write quadratic equations
Essential Question: What information does each form of a quadratic equation give you?
Words
Inequality Set Notation
Interval Notation
All real numbers
All real numbers less than 4
All real numbers less than or equal to 4
All real numbers greater than - 2
All real numbers greater than or equal to - 2
All real numbers greater than 0 and less than 5
All real numbers greater than or equal to 0 and less than or equal to 5
All real numbers greater than or equal to - 6 and less than 5
All real numbers greater than -6 and less than or equal to 5

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