05_M_GOLD_9004_12_ch04-1

# 05_M_GOLD_9004_12_ch - Chapter 4 The Exponential and Natural Logarithm Functions 4.1 Exponential Functions 1 4 x = 2 2 = 22x x x 3 =(31 2 = 3(1 2 x

This preview shows pages 1–4. Sign up to view the full content.

133 Chapter 4 The Exponential and Natural Logarithm Functions 4.1 Exponential Functions 1. ( ) 22 42 2 x xx == ( ) ( ) 1/2 (1/2) 33 3 x x x () ( ) 1 12 2 1 93 3 9 x x x x −− ⎛⎞ = ⎜⎟ ⎝⎠ 2. ( ) 27 3 3 x ( ) ( ) 1/3 (1/3) 3 2 x x x ) 1 13 3 1 82 2 8 x x x x = 3. ( ) 2/ 3 3 3 3 ( 3 ) 2 2 2 x x = ( ) 3/2 3 / 2 2 2(3 / 2) 3 3 3 x x = ( ) 3/4 4 4 (3/4 ) 3 16 2 2 2 x x = 4. ( ) /2 2 2( /2) 3 3 x x = ( ) 4/ 3 3 3 3 ( 3 ) 4 2 2 x x = ( ) 3 2 / 3 3 3( 2 / 3) 2 27 3 3 3 x x = 5. ) 2 2 21 4 1 2 4 x x x x = ) 3 3 31 9 1 2 8 x x x x = () ( ) 1 14 2 1 81 3 3 81 x x x x = 6. ) 2 2 4 1 3 9 x x x x = ( ) /3 / 3 1 3( / 3) 1 27 3 27 x x x ( ) / 2 1 4( / 2) 2 1 16 2 16 x x x 7. 63 ( 2 3 )3 33) 3 )2 xxxxx x x ⋅= =⋅ = 15 (3 5) 3 5 3 55 5 x x x x ⋅⋅ === 2 2 2 12 (3 4) 3 4 3 (2 ) 3 2 2 x x x x x x x = 8. 71 47( 7 2 ) 772 72 2 x x x x xxx x x −+ ⋅=⋅ = 2 1 3 6( 2 3 )2 x x x x x = 2 2 3 1 2 18 9 2 3 2 2 x x x x = = 9. 4 424 2 2 2 3 3 3 3 x x = = 51 ( 1) 1 ( 6 2 ++ +− +− − ( ) 2 2 2 3 2 3 27 3 3 x x x = 10. 2 1 3 2 3 x x x x x = 5 52 5 2 3 2 3 333 3 3 x x x x x + = = 4 43 4 3 7 3 16 (2 ) 2 2 8( 2 ) x x x + 11. 3 5 /2 3 (5 /2) (6 /2) (5 /2) 2 2 2 x x x x x = = 3 3 1 2 2 / 3 (6 / 3) (2 / 3) 4 / 3 (4 / 3) 1 3 3 3 3 3 x x x x x x = = 12. 5/ 4 5/4 1 4 4 (5 / 4) (4 / 4) / 4 1 2 2 2 2 x x x x x 2 4 /2 ( 4 /2) (5 /2) 3 3 3 3 x x x x x + =

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
134 Chapter 4 The Exponential and Natural Logarithm Functions 13. ( ) ( ) () 2/5 32 3 2 52 22 2 xx x x −− ⋅= == ( ) () () ()( ) /9 1/2 4 1/ 2 4 2 2 / 9/ 9 18 1 8 9 99 3 3 33 3 x x x x + ⎛⎞ ⎜⎟ ⎝⎠ =⋅ = 14. ( ) 5 /5 5 ( /5)5 5 54 3 3 x x x −+ ( ) 3 31 / 4 3 / 4 1/4 3/4 4 4 13 1 3 3 26 16 16 2 2 2 x x x x = 15. 11 () 3 3 x x x fx b = = 16. /3 1/3 88 x x x b = 17. 552 2 1 x =⇒=⇒= 18. 2 10 10 2 2 x =⇒ = = 19. 21 5 51 (2.5) (2.5) 2 1 5 2 2 x + + = = = 20. 35 (3.2) (3.2) 3 5 8 x = = 21. 2 10 100 10 10 1 2 1 x x = =− 22. 44 3 28 43 1 = ⇒−=⇒= 23. 55 3(2.7) 8.1 2.7 2.7 5 1 1 5 x x =⇒= = 24. 4(2.7) 10.8 2.7 2.7 1 1 2 = + −=⇒ = = 25. ( ) ( ) 1 3 2 4 2 2 2 2 4 1 41 5 x x +− + = =⇒ −=⇒ + 26. ( ) ( ) 2 2 8 8 3 3 3 7 1 x ++ = = +=⇒= = 27. 3 2 5 5 24 2 2 3 2 52 2 1 x x x x + =⋅ ⇒ = ⋅ ⇒ = + = 28. 3330 3 1 1 61 6 x x + ⋅ −=⇒ =⇒ +=⇒ =⇒ = 29. ( ) 125 2 0 2 1 5 0 2( 4 )0 x x x = ⇒+ = −= Since 2 0 x for every x , then 4 x = is the only solution. 30. (2 3 )5 4 5 0 5 (2 3 4) 0 5( 6 3) 0 x x x = + = Since 5 0 x for every x , x = 2 is the only solution. 31. 3 82 20 022 1 x =− ⇒= 32. 1 2 2 0 2 2 2 0 x x x x xxx ⇒− = ⇒= =− ⇒ = 33. ( ) 2 2 2 8 02 6 2 8 0 x x −⋅ +=⇒ −⋅ += 2 Let 2 6 8 0 ) (4 ) 0 2 , 4 o r 1 o r 2 x XX X X X + = = = = = = 34. 7 2 4 0 (2 ) 2 17 2 4 0 + −⋅+=⇒ −⋅+= 2 2 Let 2 4 17 4 0 17 17 4(4)(4) 1 ,4 84 1 2 or 2 4 2 or 2 4 x X X + = ±− − = = = = 35. 3 1 23 2 7 0 ( 3) 1 2 x x −⋅+ =⇒ −⋅+ = 2 Let 3 12 27 0 (3 ) (9 ) 0 3 , 9 o r 39 1 o r 2 x X X X =⇒ − +=⇒ = = = = =
Section 4.2 The Exponential Function e x 135 36. 22 2 4 23 20( 2 )4 20 xx x x −⋅ − =⇒ −⋅ − = 2 Let 2 4 32 0 (4 ) (8 ) 0 4 , 8 2 4 (no solution) or 2 8 3 x XX X X X x =⇒ −= +− = = = =− = ⇒ = 37.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 04/24/2010 for the course MATH 9374 taught by Professor Smith during the Spring '10 term at University of California, Berkeley.

### Page1 / 27

05_M_GOLD_9004_12_ch - Chapter 4 The Exponential and Natural Logarithm Functions 4.1 Exponential Functions 1 4 x = 2 2 = 22x x x 3 =(31 2 = 3(1 2 x

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online