Notes Day 8.3 PAP Algebra 2 Objective: TLW… develop the definition of logarithms by exploring and describing the relationship between exponential.

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Notes Day 8.3 PAP Algebra 2 Objective: TLW… develop the definition of logarithms by exploring and describing the relationship between exponential functions and their inverses (2A.11.A) Solve exponential/logarithmic equations using algebraic methods (2A.11.D) use laws of exponents to relate the properties for logarithms Describe limitations on domain and ranges(2A.11.B)

Properties of Exponents v Properties of Logarithms PRODUCT QUOTIENT POWER

Note we are simplifying not solving for x! Rewrite each expression as a single logarithm log818 – log86 1. log8 y = log b x log83 Note we are simplifying not solving for x!

Note we are simplifying not solving for x! Rewrite each expression as a single logarithm log43 + 2log4x + 3log4y 2. log43 + log4x2 + log4y3 y3 = log b x log4(3x2y3) Note we are simplifying not solving for x!

Note we are simplifying not solving for x! Rewrite each expression as a single logarithm 3. log x + log x – 2 log x Which btw means 10 0=1 so the simplified answer is 0...but we were asked for a log log y3 = log b x log 1 Note we are simplifying not solving for x!

Note we are solving for x !! Find the value of x in each logarithmic equation 4. log316 + log325=log3x log316 + log325 =log3x y3 = log b x log3 (16 25 )=log3x Note we are solving for x !! log3 (2 5)=log3x log3 (10)=log3x

y3 = log b x SOLVE for x in each logarithmic equation 5. log33 = log3x – log33 y3 = log b x

y3 = log b x SOLVE for x in each logarithmic equation 6. log427 – (2log46 – log481)=log4x y3 = log b x

Solve for x: 7. 8. But x = – 6 is not in the reasonable domain

Special Logarithm Values x x logabx=_____ xlogab logaax=___ Change to exp Change to log log power rule

Find the inverse of each function 9. y = log7x3 x = 3log7y y = log b x

y = log b x 10. 11. Find the inverse of each function y = log(x+1) 10. 11. y = log(x+1) y = log(10x) y = log b x x = log(10y) x = log(y+1) 10x =10y 10x = y+1 10x – 1 = y 10(x-1) =y

12. Find the domain and range of Look above at the parent function of y = log x Parent Function Y=log x X Y 0.1 -1 1 10 10y = x 3 Domain: ________ Range: _________ V. Asymptote: _______ 1 All reals y

Activity: Now lets see what you know. I will show you some problems. When I ask for the answer, please show the color of the matching correct answer.

Solve for x: A. -36 B. 3 C. 6 D. 28

Solve for x: A. 28 B. 30 C. 60 D. 75

Solve for x: A. 3 B. 4 C. 19 D. 29

Solve for x: A. 1 B. 3 C. 1/3 D. 0

Solve for x: A. 3 B. 6 C. 9 D. 81

Solve for x: A. -36 B. 3 C. 6 D. 28

Solve for x: A. 1 B. 2 C. 9 D. 20

Solve for x: A. 1/5 B. 2 C. 32 D. 10

Solve for x: A. -27 B. -4 C. 9 D. 27

Solve for x: A. 3 B. 5 C. 2/3 D. 30