1 / 27

Properties of Exponents v Properties of Logarithms

armine
Download Presentation

Properties of Exponents v Properties of Logarithms

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related