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Properties of Exponents v Properties of Logarithms

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Properties of Exponents v Properties of Logarithms

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  1. Notes Day 8.3 PAP Algebra 2Objective: 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)

  2. Properties of Exponents v Properties of Logarithms PRODUCT QUOTIENT POWER

  3. Rewrite each expression as a single logarithm log108 + 2 log10x log818 – log86 1. 2. log108 + log10x2 log8 y = log b x Log10(8x2) log83 Note we are simplifying not solving for x!

  4. Rewrite each expression as a single logarithm log43 + 2log4x + 3log4y 5log2x – 3log2x 3. 4. log43 + log4x2 + log4y3 log2x5 – log2x3 y3 = log b x log4(3x2y3) log2 log2 Note we are simplifying not solving for x!

  5. Rewrite each expression as a single logarithm log4y + 2 log4y logx + log x – 2 log x 5. 6. log4y + log4y2 log y3 = log b x Which btw means 10 0=1 so the simplified answer is 0...but we were asked for a log log4(y3) log 1 Note we are simplifying not solving for x!

  6. Find the value of x in each logarithmic equation log2x + log25=4 x log4 8 = 3 log2(5x)=4 log4 8x = 3 y3 = log b x Note we are solving for x !!

  7. Find the value of x in each logarithmic equation log316 + log325=log3x log9 x = log9 x= log316 + log325 =log3x y3 = log b x log3 (16 25 )=log3x log3 (2 5)=log3x Note we are solving for x !! log3 (10)=log3x

  8. SOLVE for x in each logarithmic equation log3(x-2)=3 log4 x = log44 y3 = log b x

  9. SOLVE for x in each logarithmic equation log33 = log3x – log33 log5 + log20 = x y3 = log b x

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

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

  12. Find the inverse of each function y = log4x y = log5x2 1. 2. y = log b x x = log4y 4x = y

  13. Find the inverse of each function y = logx y = log7x3 3. 4. x = 3log7y y = log b x x = log10y 10x = y

  14. Find the inverse of each function y = log(x+1) y = log(10x) 5. 6. x = log(10y) y = log b x x = log(y+1) 10x =10y 10x = y+1 10x – 1 = y 10(x-1) =y

  15. Find the domain and range of Look above at the parentfunction of y = logx 10y = x 3 Domain: ________ Range: _________ V. Asymptote: _______ 1 All reals y

  16. Find the domain and range of Look above at the parentfunction of y = logx Domain: ________ Range: __________ V. Asymptote: ________ 3 All reals y

  17. 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. HW : WS 8.3 – which is is due next class. We will also be taking a quiz next class on these concepts.

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

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

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

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

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

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

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

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

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

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

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