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15.4 Logs of Products and Quotients

15.4 Logs of Products and Quotients. OBJ:  To expand the logarithm of a product or quotient  To simplify a sum or difference of logarithms. What do you with the exponents when they are inside parenthesis?. (x 3 )(x 4 ) You add them!! ( I nside— A dd) (x 3 )(x 4 )

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15.4 Logs of Products and Quotients

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  1. 15.4 Logs of Products and Quotients OBJ:  To expand the logarithm of a product or quotient  To simplify a sum or difference of logarithms

  2. What do you with the exponents when they are inside parenthesis? (x3)(x4) You add them!! (Inside—Add) (x3)(x4) x(3 + 4) x7

  3. DEF:  (1) Logb of a product logb(x · y) = logbx + logby Inside parenthesis—Add logs

  4. What do you with the exponents when they are in a quotient? x3 x4 You subtract them! (Quotient—Subtract) x3 x4 x(3 – 4)

  5. DEF:  (2) Logb of a quotient logb(x / y) = logbx – logby Quotient—Subtract logs

  6. HW 5 p399( 2, 4, 6, 24, 26)P397 EX: 1 Expand log 3 (5c/d) How many log 3 do I need to write? log 3 log 3 log 3 log 3 ___ log 3 5 + log 3 c – log 3  – log 3 d

  7. EX:  Expand log b (7m/3n) log b 7 + log b m – log b 3 –log b n

  8. HW 5 P 399 (10, 12,14, 28)P398EX:3Write as one logarithm: log 37 + log 3 t – log 34 – log 3v log 3 (7t 4v)

  9. EX:  Write as one logarithm: log 2 9 + log 2 3c – log 2 c – log 25c log 2 (27c 5c2)= log 2 (27 5c)

  10. 15.5 Logs of Powers and Radicals OBJ:  To expand a logarithm of a power or a radical  To simplify a multiple of a logarithm

  11. What do you with the exponents when they are Outside parenthesis? (x3)4 You multiply them!! (Outside—multiply) (x3)4 x34 x12

  12. DEF:  (3) Logb of a power Logb(x)r = r logb (x) Outside—Multiply(out in front of log)

  13. HW 5 P402 ( 2, 4, 6, 26, 28)P 400 EX1:Expand log 5 (mn 3 ) 2 How many log 5 do I write in the parenthesis and with what symbol in between? (log 5 m + log 5 n) Where does the outside exponent of 2 and the inside exponent of 3 go? 2 (log 5 m + 3log 5 n)

  14. P400 EX : 1 Expandlog b4(m3/ n) What does 4 (read as fourth root) become out in front of the parenthesis and what symbol is separating the terms in the parenthesis? ( )( – ) (1/4)(3log b m – log b n)

  15. HW5 P402 (10,12,14,32,34)P401EX:3Write as one log: 5 log 2 c + 3 log 2 d log 2 (c5d3) EX:4 1/3(log5 t + 4 log5 v – log5 w) log 5 3tv4/w

  16. EX:  Expand log 2 (5c2 / d ) 3 3(log 2 5 + 2log 2 c – log 2 d) log 53 4x 2 (1/3)(log 5 4 + 2log 5 x)

  17. EX:  Write as one log: 3 log 2 t + ½ log 2 5 – 4 log 2 v log 2 (t35 /v4) (1/4)(log 2 3t + log 2 5v) log 2 (415tv)

  18. 2x =  2x = 2-4 x = -4 64x – 4 = (½)2x (26) x – 4 = (2-1)2x 6x – 24 = -2x 8x = 24 x = 3 Solve

  19. (¾)2x = 64 27 (¾)2x = (27)-1 (64) (¾)2x = (33)-1 (43) 2x = -3 x = -3 2 e3x = e7x – 2 3x = 7x – 2 -4x = -2 x = ½ Solve

  20. logn1 = 2 25 n2 = 1 25 n = 1 5 log√2 t = 6 (2 )6 = t 64 = t or (21/2)6 = t t = 8 Solve

  21. log2 x3 = 6 26 = x3 64 = x3 or (26)1/3 = (x3)1/3 4 = x ln (3x – 5) = 0 loge (3x – 5) = 0 e0 = 3x – 5 1 = 3x – 5 6 = 3x 2 = x Solve

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