home *** CD-ROM | disk | FTP | other *** search
Unknown | 1996-05-22 | 4.0 KB |
open in:
MacOS 8.1
|
Win98
|
DOS
view JSON data
|
view as text
This file was not able to be converted.
This format is not currently supported by dexvert.
Confidence | Program | Detection | Match Type | Support
|
---|
1%
| dexvert
| Eclipse Tutorial (other/eclipseTutorial)
| ext
| Unsupported |
1%
| dexvert
| JuggleKrazy Tutorial (other/juggleKrazyTutorial)
| ext
| Unsupported |
100%
| file
| data
| default
| |
100%
| gt2
| Kopftext: 'TUTOR 06'
| default (weak)
|
|
hex view+--------+-------------------------+-------------------------+--------+--------+
|00000000| 54 55 54 4f 52 20 30 36 | a1 0f 00 00 85 00 00 00 |TUTOR 06|........|
|00000010| 53 65 63 74 69 6f 6e 20 | 35 2e 32 20 20 4c 6f 67 |Section |5.2 Log|
|00000020| 61 72 69 74 68 6d 69 63 | 20 46 75 6e 63 74 69 6f |arithmic| Functio|
|00000030| 6e 73 20 61 6e 64 20 54 | 68 65 69 72 20 47 72 61 |ns and T|heir Gra|
|00000040| 70 68 73 0d 0a 00 46 6f | 72 20 6d 6f 72 65 20 70 |phs...Fo|r more p|
|00000050| 72 61 63 74 69 63 65 3a | 0d 0a 00 0d 0b 00 20 20 |ractice:|...... |
|00000060| 20 20 20 10 35 2d 32 2d | 33 0e 78 35 2d 32 0e 45 | .5-2-|3.x5-2.E|
|00000070| 78 65 72 63 69 73 65 73 | 0f 0d 0a 00 20 20 20 20 |xercises|.... |
|00000080| 20 10 35 2d 32 2d 32 0e | 65 35 2d 32 0e 47 75 69 | .5-2-2.|e5-2.Gui|
|00000090| 64 65 64 20 45 78 65 72 | 63 69 73 65 73 0f 0d 0a |ded Exer|cises...|
|000000a0| 00 0d 0a 00 54 6f 70 69 | 63 73 20 66 6f 72 20 65 |....Topi|cs for e|
|000000b0| 78 70 6c 6f 72 61 74 69 | 6f 6e 3a 0d 0a 00 0d 0b |xplorati|on:.....|
|000000c0| 00 20 20 20 20 20 0e 73 | 35 2d 32 2d 31 0e 44 65 |. .s|5-2-1.De|
|000000d0| 66 69 6e 69 74 69 6f 6e | 20 6f 66 20 61 20 4c 6f |finition| of a Lo|
|000000e0| 67 61 72 69 74 68 6d 69 | 63 20 46 75 6e 63 74 69 |garithmi|c Functi|
|000000f0| 6f 6e 0f 0d 0a 00 20 20 | 20 20 20 0e 73 35 2d 32 |on.... | .s5-2|
|00000100| 2d 32 0e 50 72 6f 70 65 | 72 74 69 65 73 20 6f 66 |-2.Prope|rties of|
|00000110| 20 4c 6f 67 61 72 69 74 | 68 6d 73 0f 0d 0a 00 20 | Logarit|hms.... |
|00000120| 20 20 20 20 0e 73 35 2d | 32 2d 33 0e 54 68 65 20 | .s5-|2-3.The |
|00000130| 47 72 61 70 68 20 6f 66 | 20 61 20 4c 6f 67 61 72 |Graph of| a Logar|
|00000140| 69 74 68 6d 69 63 20 46 | 75 6e 63 74 69 6f 6e 0f |ithmic F|unction.|
|00000150| 0d 0a 00 20 20 20 20 20 | 0e 73 35 2d 32 2d 34 0e |... |.s5-2-4.|
|00000160| 54 68 65 20 4e 61 74 75 | 72 61 6c 20 4c 6f 67 61 |The Natu|ral Loga|
|00000170| 72 69 74 68 6d 69 63 20 | 46 75 6e 63 74 69 6f 6e |rithmic |Function|
|00000180| 0f 0d 0a 00 53 65 63 74 | 69 6f 6e 20 35 2e 32 20 |....Sect|ion 5.2 |
|00000190| 20 4c 6f 67 61 72 69 74 | 68 6d 69 63 20 46 75 6e | Logarit|hmic Fun|
|000001a0| 63 74 69 6f 6e 73 20 61 | 6e 64 20 54 68 65 69 72 |ctions a|nd Their|
|000001b0| 20 47 72 61 70 68 73 0d | 0b 00 4c 6f 6f 6b 69 6e | Graphs.|..Lookin|
|000001c0| 67 20 62 61 63 6b 20 61 | 74 20 74 68 65 20 67 72 |g back a|t the gr|
|000001d0| 61 70 68 73 20 6f 66 20 | 74 68 65 20 65 78 70 6f |aphs of |the expo|
|000001e0| 6e 65 6e 74 69 61 6c 20 | 66 75 6e 63 74 69 6f 6e |nential |function|
|000001f0| 73 20 69 6e 74 72 6f 64 | 75 63 65 64 20 69 6e 20 |s introd|uced in |
|00000200| 53 65 63 74 69 6f 6e 0d | 0a 00 20 20 20 20 20 20 |Section.|.. |
|00000210| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000220| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000230| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 11 32 | | .2|
|00000240| 78 0d 0b 00 11 31 35 2e | 31 2c 20 77 65 20 73 65 |x....15.|1, we se|
|00000250| 65 20 74 68 61 74 20 65 | 76 65 72 79 20 66 75 6e |e that e|very fun|
|00000260| 63 74 69 6f 6e 20 6f 66 | 20 74 68 65 20 66 6f 72 |ction of| the for|
|00000270| 6d 20 11 33 66 11 31 28 | 11 33 78 11 31 29 20 3d |m .3f.1(|.3x.1) =|
|00000280| 20 11 33 61 20 20 11 31 | 70 61 73 73 65 73 20 74 | .3a .1|passes t|
|00000290| 68 65 20 22 68 6f 72 69 | 7a 6f 6e 74 61 6c 0d 0a |he "hori|zontal..|
|000002a0| 00 0d 0b 00 6c 69 6e 65 | 20 74 65 73 74 2c 22 20 |....line| test," |
|000002b0| 61 6e 64 20 74 68 65 72 | 65 66 6f 72 65 20 6d 75 |and ther|efore mu|
|000002c0| 73 74 20 68 61 76 65 20 | 61 6e 20 69 6e 76 65 72 |st have |an inver|
|000002d0| 73 65 2e 20 20 57 65 20 | 63 61 6c 6c 20 74 68 69 |se. We |call thi|
|000002e0| 73 20 69 6e 76 65 72 73 | 65 20 66 75 6e 63 74 69 |s invers|e functi|
|000002f0| 6f 6e 0d 0a 00 0d 0b 00 | 74 68 65 20 12 31 6c 6f |on......|the .1lo|
|00000300| 67 61 72 69 74 68 6d 69 | 63 20 66 75 6e 63 74 69 |garithmi|c functi|
|00000310| 6f 6e 20 77 69 74 68 20 | 62 61 73 65 20 11 33 61 |on with |base .3a|
|00000320| 11 31 12 30 20 61 6e 64 | 20 77 65 20 64 65 66 69 |.1.0 and| we defi|
|00000330| 6e 65 20 69 74 20 61 73 | 20 66 6f 6c 6c 6f 77 73 |ne it as| follows|
|00000340| 2e 0d 0a 00 0d 0a 00 46 | 6f 72 20 11 33 78 20 11 |.......F|or .3x .|
|00000350| 31 3e 20 30 20 61 6e 64 | 20 30 20 3c 20 11 33 61 |1> 0 and| 0 < .3a|
|00000360| 20 11 34 3d 20 11 31 31 | 2c 20 0d 0a 00 20 20 20 | .4= .11|, ... |
|00000370| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000380| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000390| 20 20 20 20 20 20 11 32 | 79 0d 0b 00 20 20 20 20 | .2|y... |
|000003a0| 20 11 33 79 20 3d 20 11 | 31 6c 6f 67 20 11 33 78 | .3y = .|1log .3x|
|000003b0| 20 20 20 20 11 31 69 66 | 20 61 6e 64 20 6f 6e 6c | .1if| and onl|
|000003c0| 79 20 69 66 20 20 20 20 | 11 33 78 20 3d 20 61 20 |y if |.3x = a |
|000003d0| 2e 0d 0b 00 20 20 20 20 | 20 20 20 20 20 20 20 20 |.... | |
|000003e0| 11 32 61 0d 0a 00 11 31 | 54 68 65 20 66 75 6e 63 |.2a....1|The func|
|000003f0| 74 69 6f 6e 20 67 69 76 | 65 6e 20 62 79 20 0d 0a |tion giv|en by ..|
|00000400| 00 0d 0b 00 20 20 20 20 | 20 11 33 66 28 78 29 20 |.... | .3f(x) |
|00000410| 3d 20 11 31 6c 6f 67 20 | 11 33 78 0d 0b 00 20 20 |= .1log |.3x... |
|00000420| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 11 32 61 | | .2a|
|00000430| 0d 0a 00 11 31 69 73 20 | 63 61 6c 6c 65 64 20 74 |....1is |called t|
|00000440| 68 65 20 6c 6f 67 61 72 | 69 74 68 6d 69 63 20 66 |he logar|ithmic f|
|00000450| 75 6e 63 74 69 6f 6e 20 | 77 69 74 68 20 62 61 73 |unction |with bas|
|00000460| 65 20 11 33 61 11 31 2e | 0d 0a 00 0d 0b 00 20 20 |e .3a.1.|...... |
|00000470| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000480| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000490| 20 20 20 20 20 20 11 32 | 78 0d 0b 00 11 31 53 69 | .2|x....1Si|
|000004a0| 6e 63 65 20 6c 6f 67 20 | 11 33 78 20 11 31 69 73 |nce log |.3x .1is|
|000004b0| 20 74 68 65 20 69 6e 76 | 65 72 73 65 20 66 75 6e | the inv|erse fun|
|000004c0| 63 74 69 6f 6e 20 6f 66 | 20 11 33 61 20 11 31 2c |ction of| .3a .1,|
|000004d0| 20 69 74 20 66 6f 6c 6c | 6f 77 73 20 74 68 61 74 | it foll|ows that|
|000004e0| 20 74 68 65 20 64 6f 6d | 61 69 6e 20 6f 66 20 0d | the dom|ain of .|
|000004f0| 0b 00 20 20 20 20 20 20 | 20 20 20 11 32 61 0d 0b |.. | .2a..|
|00000500| 00 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |. | |
|00000510| 20 20 20 20 20 20 20 20 | 78 0d 0b 00 11 31 6c 6f | |x....1lo|
|00000520| 67 20 11 33 78 20 11 31 | 69 73 20 74 68 65 20 72 |g .3x .1|is the r|
|00000530| 61 6e 67 65 20 6f 66 20 | 11 33 61 20 11 31 2c 20 |ange of |.3a .1, |
|00000540| 74 68 61 74 20 69 73 20 | 28 30 2c 20 11 34 38 11 |that is |(0, .48.|
|00000550| 31 29 2e 0d 0b 00 20 20 | 20 11 32 61 20 20 20 20 |1).... | .2a |
|00000560| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000570| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000580| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000590| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000005a0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000005b0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000005c0| 11 31 2e 0d 0a 00 53 65 | 63 74 69 6f 6e 20 35 2e |.1....Se|ction 5.|
|000005d0| 32 20 20 4c 6f 67 61 72 | 69 74 68 6d 69 63 20 46 |2 Logar|ithmic F|
|000005e0| 75 6e 63 74 69 6f 6e 73 | 20 61 6e 64 20 54 68 65 |unctions| and The|
|000005f0| 69 72 20 47 72 61 70 68 | 73 0d 0b 00 54 68 65 20 |ir Graph|s...The |
|00000600| 66 6f 6c 6c 6f 77 69 6e | 67 20 12 31 70 72 6f 70 |followin|g .1prop|
|00000610| 65 72 74 69 65 73 20 6f | 66 20 6c 6f 67 61 72 69 |erties o|f logari|
|00000620| 74 68 6d 73 12 30 20 66 | 6f 6c 6c 6f 77 20 64 69 |thms.0 f|ollow di|
|00000630| 72 65 63 74 6c 79 20 66 | 72 6f 6d 20 74 68 65 20 |rectly f|rom the |
|00000640| 64 65 66 69 6e 69 74 69 | 6f 6e 20 0d 0a 00 6f 66 |definiti|on ...of|
|00000650| 20 74 68 65 20 6c 6f 67 | 61 72 69 74 68 6d 69 63 | the log|arithmic|
|00000660| 20 66 75 6e 63 74 69 6f | 6e 20 77 69 74 68 20 62 | functio|n with b|
|00000670| 61 73 65 20 11 33 61 11 | 31 2e 0d 0a 00 0d 0b 00 |ase .3a.|1.......|
|00000680| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000690| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 11 32 30 | | .20|
|000006a0| 0d 0b 00 20 11 31 31 2e | 20 20 6c 6f 67 20 31 20 |... .11.| log 1 |
|000006b0| 3d 20 30 20 20 20 20 20 | 20 62 65 63 61 75 73 65 |= 0 | because|
|000006c0| 20 11 33 61 20 20 11 31 | 3d 20 31 2e 0d 0b 00 20 | .3a .1|= 1.... |
|000006d0| 20 20 20 20 20 20 20 11 | 32 61 0d 0a 00 20 20 20 | .|2a... |
|000006e0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000006f0| 20 20 20 20 20 20 20 20 | 20 20 31 0d 0b 00 20 11 | | 1... .|
|00000700| 31 32 2e 20 20 6c 6f 67 | 20 11 33 61 20 11 31 3d |12. log| .3a .1=|
|00000710| 20 31 20 20 20 20 20 20 | 62 65 63 61 75 73 65 20 | 1 |because |
|00000720| 11 33 61 20 20 3d 20 61 | 11 31 2e 0d 0b 00 20 20 |.3a = a|.1.... |
|00000730| 20 20 20 20 20 20 11 32 | 61 0d 0a 00 20 20 20 20 | .2|a... |
|00000740| 20 20 20 20 20 20 78 20 | 20 20 20 20 20 20 20 20 | x | |
|00000750| 20 20 20 20 20 20 20 20 | 20 78 20 20 20 20 78 0d | | x x.|
|00000760| 0b 00 20 11 31 33 2e 20 | 20 6c 6f 67 20 11 33 61 |.. .13. | log .3a|
|00000770| 20 20 11 31 3d 20 11 33 | 78 20 20 20 20 20 11 31 | .1= .3|x .1|
|00000780| 62 65 63 61 75 73 65 20 | 11 33 61 20 20 3d 20 61 |because |.3a = a|
|00000790| 20 11 31 2e 0d 0b 00 20 | 20 20 20 20 20 20 20 11 | .1.... | .|
|000007a0| 32 61 0d 0a 00 0d 0b 00 | 20 11 31 34 2e 20 20 49 |2a......| .14. I|
|000007b0| 66 20 6c 6f 67 20 11 33 | 78 20 11 31 3d 20 6c 6f |f log .3|x .1= lo|
|000007c0| 67 20 11 33 79 11 31 2c | 20 74 68 65 6e 20 11 33 |g .3y.1,| then .3|
|000007d0| 78 20 11 31 3d 20 11 33 | 79 11 31 2e 0d 0b 00 20 |x .1= .3|y.1.... |
|000007e0| 20 20 20 20 20 20 20 20 | 20 20 11 32 61 20 20 20 | | .2a |
|000007f0| 20 20 20 20 61 0d 0a 00 | 0d 0a 00 11 31 54 68 65 | a...|....1The|
|00000800| 20 6c 6f 67 61 72 69 74 | 68 6d 69 63 20 66 75 6e | logarit|hmic fun|
|00000810| 63 74 69 6f 6e 20 77 69 | 74 68 20 62 61 73 65 20 |ction wi|th base |
|00000820| 31 30 20 69 73 20 63 61 | 6c 6c 65 64 20 74 68 65 |10 is ca|lled the|
|00000830| 20 12 31 63 6f 6d 6d 6f | 6e 20 6c 6f 67 61 72 69 | .1commo|n logari|
|00000840| 74 68 6d 69 63 12 30 0d | 0a 00 20 20 20 20 20 20 |thmic.0.|.. |
|00000850| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000860| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000870| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000880| 20 20 20 20 20 20 11 34 | 5b 32 32 32 5d 0d 0b 00 | .4|[222]...|
|00000890| 11 31 12 31 66 75 6e 63 | 74 69 6f 6e 12 30 2e 20 |.1.1func|tion.0. |
|000008a0| 20 4f 6e 20 6d 6f 73 74 | 20 63 61 6c 63 75 6c 61 | On most| calcula|
|000008b0| 74 6f 72 73 2c 20 74 68 | 69 73 20 66 75 6e 63 74 |tors, th|is funct|
|000008c0| 69 6f 6e 20 69 73 20 64 | 65 6e 6f 74 65 64 20 62 |ion is d|enoted b|
|000008d0| 79 20 11 34 21 11 31 6c | 6f 67 11 34 21 11 31 2e |y .4!.1l|og.4!.1.|
|000008e0| 0d 0b 00 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |... | |
|000008f0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000900| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000910| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 11 | | .|
|00000920| 34 6c 32 32 32 6a 20 20 | 20 20 20 20 20 20 20 20 |4l222j | |
|00000930| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000940| 20 20 20 20 20 20 20 20 | 20 20 11 31 2e 0d 0a 00 | | .1....|
|00000950| 53 65 63 74 69 6f 6e 20 | 35 2e 32 20 20 4c 6f 67 |Section |5.2 Log|
|00000960| 61 72 69 74 68 6d 69 63 | 20 46 75 6e 63 74 69 6f |arithmic| Functio|
|00000970| 6e 73 20 61 6e 64 20 54 | 68 65 69 72 20 47 72 61 |ns and T|heir Gra|
|00000980| 70 68 73 0d 0b 00 20 20 | 20 20 20 20 20 20 20 20 |phs... | |
|00000990| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 12 31 54 | | .1T|
|000009a0| 68 65 20 47 72 61 70 68 | 20 6f 66 20 61 20 4c 6f |he Graph| of a Lo|
|000009b0| 67 61 72 69 74 68 6d 69 | 63 20 46 75 6e 63 74 69 |garithmi|c Functi|
|000009c0| 6f 6e 12 30 0d 0a 00 0d | 0b 00 47 72 61 70 68 20 |on.0....|..Graph |
|000009d0| 6f 66 20 11 33 79 20 11 | 31 3d 20 6c 6f 67 20 11 |of .3y .|1= log .|
|000009e0| 33 78 2c 20 61 20 3e 20 | 31 0d 0b 00 20 20 20 20 |3x, a > |1... |
|000009f0| 20 20 20 20 20 20 20 20 | 20 20 20 20 11 32 61 0d | | .2a.|
|00000a00| 0a 00 11 34 2e 20 11 31 | 44 6f 6d 61 69 6e 3a 20 |...4. .1|Domain: |
|00000a10| 28 30 2c 20 11 34 38 11 | 31 29 20 20 20 20 20 20 |(0, .48.|1) |
|00000a20| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000a30| 20 14 74 2d 36 2d 32 2d | 31 2e 68 69 14 34 30 14 | .t-6-2-|1.hi.40.|
|00000a40| 34 14 32 35 14 39 14 0d | 0a 00 11 34 2e 20 11 31 |4.25.9..|...4. .1|
|00000a50| 52 61 6e 67 65 3a 20 28 | 2d 11 34 38 11 31 2c 20 |Range: (|-.48.1, |
|00000a60| 11 34 38 11 31 29 0d 0a | 00 11 34 2e 20 11 31 49 |.48.1)..|..4. .1I|
|00000a70| 6e 74 65 72 63 65 70 74 | 3a 20 28 31 2c 20 30 29 |ntercept|: (1, 0)|
|00000a80| 0d 0a 00 11 34 2e 20 11 | 31 49 6e 63 72 65 61 73 |....4. .|1Increas|
|00000a90| 69 6e 67 0d 0a 00 11 34 | 2e 20 11 33 79 11 31 2d |ing....4|. .3y.1-|
|00000aa0| 61 78 69 73 20 69 73 20 | 61 20 76 65 72 74 69 63 |axis is |a vertic|
|00000ab0| 61 6c 20 61 73 79 6d 70 | 74 6f 74 65 0d 0a 00 20 |al asymp|tote... |
|00000ac0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000ad0| 20 20 20 20 20 20 20 11 | 32 2b 0d 0b 00 20 20 11 | .|2+... .|
|00000ae0| 31 28 6c 6f 67 20 11 33 | 78 20 11 34 32 33 20 11 |1(log .3|x .423 .|
|00000af0| 31 2d 11 34 38 20 11 31 | 61 73 20 11 33 78 20 11 |1-.48 .1|as .3x .|
|00000b00| 34 32 33 20 11 31 30 20 | 29 0d 0b 00 20 20 20 20 |423 .10 |)... |
|00000b10| 20 20 11 32 61 0d 0a 00 | 11 34 2e 20 11 31 43 6f | .2a...|.4. .1Co|
|00000b20| 6e 74 69 6e 75 6f 75 73 | 0d 0b 00 20 20 20 20 20 |ntinuous|... |
|00000b30| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000b40| 20 20 20 20 20 20 20 20 | 20 11 32 78 0d 0b 00 11 | | .2x....|
|00000b50| 34 2e 20 11 31 52 65 66 | 6c 65 63 74 69 6f 6e 20 |4. .1Ref|lection |
|00000b60| 6f 66 20 67 72 61 70 68 | 20 6f 66 20 11 33 79 20 |of graph| of .3y |
|00000b70| 3d 20 61 0d 0a 00 20 20 | 11 31 61 62 6f 75 74 20 |= a... |.1about |
|00000b80| 74 68 65 20 6c 69 6e 65 | 20 11 33 79 20 3d 20 78 |the line| .3y = x|
|00000b90| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000ba0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000bb0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000bc0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000bd0| 11 31 2e 0d 0a 00 53 65 | 63 74 69 6f 6e 20 35 2e |.1....Se|ction 5.|
|00000be0| 32 20 20 4c 6f 67 61 72 | 69 74 68 6d 69 63 20 46 |2 Logar|ithmic F|
|00000bf0| 75 6e 63 74 69 6f 6e 73 | 20 61 6e 64 20 54 68 65 |unctions| and The|
|00000c00| 69 72 20 47 72 61 70 68 | 73 0d 0b 00 52 65 63 61 |ir Graph|s...Reca|
|00000c10| 6c 6c 20 74 68 61 74 20 | 74 68 65 20 6d 6f 73 74 |ll that |the most|
|00000c20| 20 77 69 64 65 6c 79 20 | 75 73 65 64 20 62 61 73 | widely |used bas|
|00000c30| 65 20 66 6f 72 20 65 78 | 70 6f 6e 65 6e 74 69 61 |e for ex|ponentia|
|00000c40| 6c 20 66 75 6e 63 74 69 | 6f 6e 73 20 69 73 20 74 |l functi|ons is t|
|00000c50| 68 65 20 6e 75 6d 62 65 | 72 20 0d 0a 00 11 33 65 |he numbe|r ....3e|
|00000c60| 11 31 2e 20 20 54 68 69 | 73 20 69 73 20 74 72 75 |.1. Thi|s is tru|
|00000c70| 65 20 66 6f 72 20 6c 6f | 67 61 72 69 74 68 6d 69 |e for lo|garithmi|
|00000c80| 63 20 66 75 6e 63 74 69 | 6f 6e 73 20 61 6c 73 6f |c functi|ons also|
|00000c90| 2c 20 61 6e 64 20 77 65 | 20 63 61 6c 6c 20 74 68 |, and we| call th|
|00000ca0| 65 20 6c 6f 67 61 72 69 | 74 68 6d 69 63 20 0d 0a |e logari|thmic ..|
|00000cb0| 00 66 75 6e 63 74 69 6f | 6e 20 77 69 74 68 20 62 |.functio|n with b|
|00000cc0| 61 73 65 20 11 33 65 20 | 11 31 74 68 65 20 12 31 |ase .3e |.1the .1|
|00000cd0| 6e 61 74 75 72 61 6c 20 | 6c 6f 67 61 72 69 74 68 |natural |logarith|
|00000ce0| 6d 69 63 20 66 75 6e 63 | 74 69 6f 6e 12 30 2e 20 |mic func|tion.0. |
|00000cf0| 20 46 6f 72 20 73 69 6d | 70 6c 69 63 69 74 79 20 | For sim|plicity |
|00000d00| 0d 0a 00 77 65 20 64 65 | 6e 6f 74 65 20 74 68 65 |...we de|note the|
|00000d10| 20 6e 61 74 75 72 61 6c | 20 6c 6f 67 61 72 69 74 | natural| logarit|
|00000d20| 68 6d 69 63 20 66 75 6e | 63 74 69 6f 6e 20 6f 66 |hmic fun|ction of|
|00000d30| 20 11 33 78 20 11 31 61 | 73 20 6c 6e 20 11 33 78 | .3x .1a|s ln .3x|
|00000d40| 11 31 2e 0d 0a 00 0d 0b | 00 54 68 65 20 66 75 6e |.1......|.The fun|
|00000d50| 63 74 69 6f 6e 20 64 65 | 66 69 6e 65 64 20 62 79 |ction de|fined by|
|00000d60| 20 0d 0a 00 0d 0b 00 20 | 20 20 20 20 11 33 66 28 | ...... | .3f(|
|00000d70| 78 29 20 3d 20 11 31 6c | 6f 67 20 11 33 78 20 11 |x) = .1l|og .3x .|
|00000d80| 31 3d 20 6c 6e 20 11 33 | 78 11 31 2c 20 20 11 33 |1= ln .3|x.1, .3|
|00000d90| 78 20 11 31 3e 20 30 0d | 0b 00 20 20 20 20 20 20 |x .1> 0.|.. |
|00000da0| 20 20 20 20 20 20 20 20 | 20 11 32 65 0d 0a 00 11 | | .2e....|
|00000db0| 31 69 73 20 63 61 6c 6c | 65 64 20 74 68 65 20 6e |1is call|ed the n|
|00000dc0| 61 74 75 72 61 6c 20 6c | 6f 67 61 72 69 74 68 6d |atural l|ogarithm|
|00000dd0| 69 63 20 66 75 6e 63 74 | 69 6f 6e 2e 0d 0a 00 0d |ic funct|ion.....|
|00000de0| 0a 00 54 68 65 20 66 6f | 6c 6c 6f 77 69 6e 67 20 |..The fo|llowing |
|00000df0| 12 31 70 72 6f 70 65 72 | 74 69 65 73 20 6f 66 20 |.1proper|ties of |
|00000e00| 6e 61 74 75 72 61 6c 20 | 6c 6f 67 61 72 69 74 68 |natural |logarith|
|00000e10| 6d 73 12 30 20 66 6f 6c | 6c 6f 77 20 64 69 72 65 |ms.0 fol|low dire|
|00000e20| 63 74 6c 79 20 66 72 6f | 6d 20 74 68 65 20 0d 0a |ctly fro|m the ..|
|00000e30| 00 64 65 66 69 6e 69 74 | 69 6f 6e 2e 0d 0a 00 0d |.definit|ion.....|
|00000e40| 0b 00 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |.. | |
|00000e50| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 11 32 | | .2|
|00000e60| 30 0d 0b 00 20 11 31 31 | 2e 20 20 6c 6e 20 31 20 |0... .11|. ln 1 |
|00000e70| 3d 20 30 20 20 20 20 20 | 20 62 65 63 61 75 73 65 |= 0 | because|
|00000e80| 20 11 33 65 20 20 11 31 | 3d 20 31 2e 0d 0a 00 20 | .3e .1|= 1.... |
|00000e90| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000ea0| 20 20 20 20 20 20 20 20 | 20 20 20 11 32 31 0d 0b | | .21..|
|00000eb0| 00 20 11 31 32 2e 20 20 | 6c 6e 20 11 33 65 20 11 |. .12. |ln .3e .|
|00000ec0| 31 3d 20 31 20 20 20 20 | 20 20 62 65 63 61 75 73 |1= 1 | becaus|
|00000ed0| 65 20 11 33 65 20 20 11 | 31 3d 20 11 33 65 11 31 |e .3e .|1= .3e.1|
|00000ee0| 2e 0d 0a 00 20 20 20 20 | 20 20 20 20 20 11 32 78 |.... | .2x|
|00000ef0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000f00| 20 20 78 20 20 20 20 78 | 0d 0b 00 20 11 31 33 2e | x x|... .13.|
|00000f10| 20 20 6c 6e 20 11 33 65 | 20 20 11 31 3d 20 11 33 | ln .3e| .1= .3|
|00000f20| 78 20 20 20 20 20 11 31 | 62 65 63 61 75 73 65 20 |x .1|because |
|00000f30| 11 33 65 20 20 3d 20 65 | 20 11 31 2e 20 20 20 20 |.3e = e| .1. |
|00000f40| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000f50| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000f60| 20 20 20 20 20 20 20 2e | 0d 0a 00 0d 0b 00 20 34 | .|...... 4|
|00000f70| 2e 20 20 49 66 20 6c 6e | 20 11 33 78 20 11 31 3d |. If ln| .3x .1=|
|00000f80| 20 6c 6e 20 11 33 79 11 | 31 2c 20 74 68 65 6e 20 | ln .3y.|1, then |
|00000f90| 11 33 78 20 11 31 3d 20 | 11 33 79 11 31 2e 0d 0a |.3x .1= |.3y.1...|
|00000fa0| 00 43 00 00 00 41 01 00 | 00 4d 33 00 00 10 00 00 |.C...A..|.M3.....|
|00000fb0| 00 00 00 00 00 73 35 2d | 32 00 b7 01 00 00 0f 04 |.....s5-|2.......|
|00000fc0| 00 00 4d 33 00 00 84 01 | 00 00 00 00 00 00 73 35 |..M3....|......s5|
|00000fd0| 2d 32 2d 31 00 f9 05 00 | 00 57 03 00 00 4d 33 00 |-2-1....|.W...M3.|
|00000fe0| 00 c6 05 00 00 00 00 00 | 00 73 35 2d 32 2d 32 00 |........|.s5-2-2.|
|00000ff0| 83 09 00 00 53 02 00 00 | 4d 33 00 00 50 09 00 00 |....S...|M3..P...|
|00001000| 00 00 00 00 73 35 2d 32 | 2d 33 00 09 0c 00 00 98 |....s5-2|-3......|
|00001010| 03 00 00 4d 33 00 00 d6 | 0b 00 00 00 00 00 00 73 |...M3...|.......s|
|00001020| 35 2d 32 2d 34 00 | |5-2-4. | |
+--------+-------------------------+-------------------------+--------+--------+