1 / 15

15.4, 5 Solving Logarithmic Equations

15.4, 5 Solving Logarithmic Equations. OBJ:  To solve a logarithmic equation. DEF:  Property of equality for logarithms. If log b x = log b y, then x = y Note: Each apparent solution must be checked since log b x is defined only when x > 0.

drake
Download Presentation

15.4, 5 Solving Logarithmic Equations

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. 15.4, 5 Solving Logarithmic Equations OBJ: To solve a logarithmic equation

  2. DEF: Property of equality for logarithms If log b x = log b y, then x = y • Note: Each apparent solution must be checked since log b x is defined only when x > 0

  3. HW 7 p399 ( 16 – 22 even) P 398 Solve EX: 5 log52t + log5 (t – 4) = log548 – log5 2 log 5 2t(t – 4) = log 5 (48 / 2) 2t(t – 4) = (48 / 2) 2t2 – 8t =24 2t2 – 8t – 24 = 0 2(t2 – 4t – 12) = 0 2(t – 6)(t + 2) = 0 t = -2, t = 6 now 

  4. Check log52t + log5 (t – 4) = log548 – log5 2 log 5 2(6) + log 5 (6 – 4) = log 5 48 – log 5 2 log 5 2(6)(6 – 4) = log 5 48/2 log 5 12(2) = log 5 48/2 log 5 24 = log 5 24 x = 6 log 5 2(-2) + log 5 (-2 – 4) = log 5 48 – log5 2 x ≠ -2 because cannot have log 5 -4

  5. Solve and check EX: log b 8t + log b 2 = log b 48 log b 8t (2) = log b 48 log b 16t = log b 48 16t = 48 t = 3 • log b 8(3) + log b 2 = log b 48 log b 8(3)(2) = log b 48 log b 48 = log b 48  t = 3

  6. Solve and Check EX: log 5 x + log 5 12 = log 5 ( x – 4) log 5 x + log 5 12 = log 5 ( x – 4) log 5 x (12) = log 5 ( x – 4) 12x = x – 4 11x = -4 x = -4/11 Ø

  7. HW 7 P402 (16, 20, 24)P 401 Solve EX:5 2 log 3 t = log 3 2 + log 3 (t + 12 ) log 3 t2 = log 3 2 (t + 12 ) t2 = 2 (t + 12 ) t2 – 2 t – 24 = 0 (t – 6) ( t + 4) = 0 t = 6, t = -4 now 

  8. Check 2 log 3 t = log 3 2 + log 3 (t + 12 ) 2 log 3 6 = log 3 2 + log 3 (6 + 12 ) log 3 62 = log 3 2(6 + 12 ) log 3 36 = log 3 2(18 ) log 3 36 = log 3 36 x = 6 2 log 3 -4 = log 3 2 + log 3 (-4 + 12 ) x ≠ -4 because cannot have 2 log 3 -4

  9. HW 7 P 402 (18, 22)P 401Solve EX:6½ log b a + ½ log b (a – 6) = log b 4 ½ (log b a(a – 6)) = log b 4 log b√a(a – 6) = log b 4 √a(a – 6) = 4 (√a(a – 6))2 = 42 a(a – 6) = 42 a2 – 6a – 16 = 0 (a – 8) (a + 2) = 0 a = 8, -2 now 

  10. Check ½ log b a + ½ log b (a – 6) = log b 4 ½ log b 8 + ½ log b (8 – 6) = log b 4 log b√8 (8 – 6) = log b 4 √8 (2) = 4 √16 = 4 x = 8 ½ log b -2 + ½ log b (-2 – 6) = log b 4 x ≠ -2 because cannot have ½ log b -2

  11. Solve EX: 2 log b x = log b 3 + log b ( x + 6 ) log b x2 = log b 3( x + 6 ) x2 = 3( x + 6 ) x2 = 3x + 18 x2 – 3x– 18 = 0 (x – 6) (x + 3) = 0 x = 6, x = -3 now 

  12. Check 2 log b x = log b 3 + log b ( x + 6 ) 2 log b 6 = log b 3 + log b ( 6 + 6 ) log b 62 = log b 3( 6 + 6 ) log b 36 = log b 3(12) log b 36 = log b 36 x = 6 2 log b -3 = log b 3 + log b ( -3 + 6 ) x ≠-3 because cannot have 2 log b -3

  13. Solve EX:  ½ log 4 x + ½ log 4 (x – 8) = log 4 3 ½ log 4 x + ½ log 4 (x – 8) = log 4 3 log 4√x(x – 8) = log 4 3 √x(x – 8) = 3 (√x(x – 8))2 = 32 x(x – 8) = 32 x2 – 8x– 9 = 0 (x– 9) (x + 1) = 0 x = 9, x = -1 now 

  14. Check ½ log 4 x + ½ log 4 (x – 8) = log 4 3 ½ log 4 9 + ½ log 4 (9 – 8) = log 4 3 log 4√9(9 – 8) = log 4 3 log 4√9(1) = log 4 3 log 43 = log 4 3 x = 9 ½ log 4 -1 + ½ log 4 (-1 – 8) = log 4 3 x ≠ -1 because cannot have ½ log 4-1

  15. NOTE: Remember if log b x =y, then b y = x EX: log 4 (3y + 1) + log 4 (y–1) = 3 log 4 (3y + 1) (y–1) = 3 43 = (3y + 1) (y–1) 64 = 3y2 – 3y + 1y – 1 3y2 – 2y– 65 = 0 (3y + 13) (y – 5) = 0 y = -13/3, y = 5  43 = (3· 5 + 1) (5 –1) 64 = (16) (4)

More Related