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W17D2 Log Practice Warm Up 9x7 1. Expand ln 3 y 2. Condense log 5 − 6 log x + 4 log y 1. ln 9 + 7 ln x − 3 ln y 2. log 1. 2. 3. 4. 5x6 y3 Change of base formula Graphing Review Pg 482 489 39 and 42 Worksheet bottom half Change of base formula EX 1: ax = b take the log of both sides log10 ax = log10 b x log10 a = log10 b divide both sides by log10 a log10 b x= log10 a rewrite starting statement in log format loga b = x log10 b loga b = log10 a EX 2: EX 3: EX 4: log10 5 = 1.46 log10 3 log4 3 1 = log3 9 = log4 9 2 64 = log2 4 = 2 log2 16 log3 5 = vs log2 64 = log16 64 = 3 log2 16 EX 8: ln 2 = .69 ln 3 = 1.1 2 = ln 2 − ln 27 = .69 − 3.3 = −2.61 ln 27 EX 9: 3x − 6 1 Expand to 3 natural logs ln( √ ) = ln 3 + ln(x − 2) − ln 5 2 5 Groupwork bottom half of the worksheet Do Regression on the calc for the lab? Groupwork bottom half of the worksheet Condense CONDENSE (skip 28, 30?) 27. log 28. SKIP log9 3 x log y5 29. 30. SKIP log6 31. √ ln z 3 xy 32. 33. 34. 35. 36. Expand 86 1130 4 11 7 106 324 log4 x3 y 9 5 a log4 b6 √ log9 z xy 4 11 log2 66 √ 3 log7 z xy EXPAND 9. 1 + 6 log6 5 1 + log4 11 + 4 log4 7 10. 2 3 11. 5 log6 c + log6 a 2 12. 10 ln 5 − 5 ln 2 18 log5 x − 6 log5 y 3 14. 3 log4 7 + log4 2 2 15. log2 y + log2 v + 2 log2 w 13. 16. 18 log9 12 + log9 7 3 17. 5 log9 c + log9 a 2 Inquiry Worksheet Bottom Half Answers 1. 2 log2 5 = 4.644 2. 2 log 6 = 5.17 3. log2 5 + log2 6 = 4.907 4. log2 53 · 6 = 9.551 5. log2 62 · 5 = 7.492 6. log2 5 · 23 = 5.322 7. log2 5 + 3 8. log4 3 + 2 9. log5 2 + 2 10. log3 2 + log3 x 11. log5 7 + 2 log5 a 12. log10 3 + log10 5 + 3 log10 x + 4 log10 y 13. log10 3 14. log10 30 15. log2 x 16. log10 x y 17. log2 18. log4 1 81x2 8x3 y2 19. log7 (7x + 3) = log7 (5x + 9) 20. log3 (x2 + x − 6) = log3 14 x=3 x=4 21. log2 (3x + 11) = 5 22. log(4x − 8) = 3 x=7 x = 252 23. log3 (6x + 3) + log2 8 = log2 128 24. log4 64 − log4 (x − 12) = log2 8 x = 13 x = 13 25. log5 (x2 + 3x) = log5 (−8 − 3x) 26. 4 log3 (−9x) = 4 x = −4 x=− 27. log3 28. − 2 log5 (x + 1) = −8 x=0 x = 624 29. log4 3x + 2 log3 9 = log4 256 30. log4 (x2 − 6x) = log4 (10 + 3x) x= 1 + log9 (x + 1) = −6 + log6 36 81 Exit Pass 1. Expand the expression and simplify log2 (32)x 2. Condense the expression and simplify log3 54 − log3 2 1. Rewrite in condensed form and simplify 2 log4 y − 2 log4 3 1 x = 12 2. Solve 2log 6 = log 27 = log x 3 log3 27 + log3 2 − log3 2 = 3 1 3 1 3 x = −1, 10