barcode generator macro excel Logarithmic Function in Software

Creator Code39 in Software Logarithmic Function

Logarithmic Function
Code 39 Extended Creation In None
Using Barcode maker for Software Control to generate, create Code 39 Extended image in Software applications.
Code 3/9 Reader In None
Using Barcode recognizer for Software Control to read, scan read, scan image in Software applications.
A logarithmic function is the inverse of an exponential function, as shown below Just as in the exponential function, a is called the base of the logarithmic function:
Generating Code-39 In C#.NET
Using Barcode printer for .NET framework Control to generate, create USS Code 39 image in VS .NET applications.
Code39 Printer In .NET Framework
Using Barcode printer for ASP.NET Control to generate, create Code 3 of 9 image in ASP.NET applications.
= c - x = lo~y
Making Code 39 In .NET Framework
Using Barcode encoder for .NET framework Control to generate, create Code 39 Extended image in Visual Studio .NET applications.
Code39 Creator In VB.NET
Using Barcode printer for Visual Studio .NET Control to generate, create Code 39 Full ASCII image in VS .NET applications.
In other words, if x is given, we can calculate y by using the exponential function~ if y is given, we can calculate x by using the logarithmic function
Draw ECC200 In None
Using Barcode creation for Software Control to generate, create Data Matrix 2d barcode image in Software applications.
Making EAN13 In None
Using Barcode encoder for Software Control to generate, create EAN13 image in Software applications.
Exponential and logarithmic functions are the inverse of each other
Barcode Creator In None
Using Barcode generation for Software Control to generate, create barcode image in Software applications.
Paint Code 128 Code Set B In None
Using Barcode creator for Software Control to generate, create Code128 image in Software applications.
Example C10
Barcode Drawer In None
Using Barcode printer for Software Control to generate, create bar code image in Software applications.
Code 39 Extended Drawer In None
Using Barcode printer for Software Control to generate, create Code 39 Full ASCII image in Software applications.
Calculate the value of the following logarithmic function,s a x b
Leitcode Generator In None
Using Barcode creation for Software Control to generate, create Leitcode image in Software applications.
Generating ANSI/AIM Code 39 In None
Using Barcode generator for Office Excel Control to generate, create Code 3 of 9 image in Office Excel applications.
= log3 9 x = log2 16
Print GS1 - 13 In Java
Using Barcode maker for Eclipse BIRT Control to generate, create EAN / UCC - 13 image in BIRT reports applications.
Linear Encoder In Visual Studio .NET
Using Barcode encoder for VS .NET Control to generate, create Linear image in VS .NET applications.
Solution
Code 39 Extended Reader In .NET
Using Barcode scanner for Visual Studio .NET Control to read, scan read, scan image in .NET framework applications.
Encode Bar Code In Java
Using Barcode drawer for Java Control to generate, create bar code image in Java applications.
We have not yet shown how to calculate the log function in different bases, but we can solve this problem intuitively a Because 32 := 9, we can say that log3 9 = 2, using the fact that the two functions are the inverse of each other b Because 24 = 16, we can say that log2l6 = 4 by using the previous fact
Recognize UCC - 12 In VB.NET
Using Barcode decoder for .NET framework Control to read, scan read, scan image in Visual Studio .NET applications.
Encode 2D Barcode In VB.NET
Using Barcode drawer for .NET framework Control to generate, create 2D Barcode image in .NET applications.
Two Common Bases
The two common bases for logarithmic functions, those that can be handled by a calculator, are base e and base 10 The logarithm in base e is normally shown as In (natural logarithm); the logarithm in base 10 is normally shown as log (omitting the base)
APPENDIX C
MATHEMATICAL REVIEW
Example Cll
Calculate the value of the following logarithmic functions a x
= log 233
b x
= In 45
Solution
For these two bases we can use a calculator
a x
= log 233 = 2367
b x
=In 45 =381
Base Transformation We often need to find the value of a logarithmic function in a base other than e or 10 If the available calculator cannot give the result in our desired base, we can use a very fundamental property of the logarithm, base transformation, as shown:
10gb Y IO&1Y= - 10gb a
Note that the right-hand side is two log functions with base b, which is different from the base a at the left-hand side This means that we can choose a base that is available in our calculator (base b) and find the log of a base that is not available (base a) Example C12
Calculate the value of the following logarithmic functions a x
=log3 810
b x = log5 600
Solution
These two bases, 3 and 5, are not available on a calculator, but we can use base 10 which is available
a x
=log3 810 = =log5 600 =
loglO 810 log 10 3 log 10 600 log 10 5
=-0477 2778
= 6095
b x
= - - = 3975
Properties of Logarithmic Functions Like an exponential function, a logarithmic function has some properties that are useful in: simplifying the calculation of a log function First:
Second:
10&1 1 = 0
10&1 a = 1
Third:
10&1 x = -10&1 x !
Fourth: Fifth: Sixth:
10&1 (x xY)
=10&1 x + lo~y
10&1 :!: = l0&z x - 10&1 y y
lo&z xY = Y x 10&1 x
APPENDIX C
MATHEMATICAL REVIEW
Example C13
Calculate the value of the following logarithmic functions a x b c x = loglO (l/10) d loga (x x y) if we know that loga x = 2 and loga y e logz (1024) without using a calculator
=log3 1 x =log3 3
Solution
We use the property of log functions to solve the problems a x b c x
=log3 1 = 0 x =log3 3 = 1
= loglO (1110) = loglOlO-l = -loglO 10 = -1
d loga (x x y) =loga x + loga Y =2 + 3 = 5 e 10gz (1024) =logz (2 10) = 10 logz 2 = 10 x 1 = 10
APPENDIXD
8B/6TCode
This appendix is a tabulation of 8B/6T code pairs The 8-bit data are shown in hexadecimal format The 6T code is shown as + (positive signal), - (negative signal), and 0 (lack of signal) notation
Table Dl 8B/6T code
Data
00 01 02
Code
Data
20 21 22 23 24 25 26 27 28 29 2A 2B 2C 2D 2E 2F 30 31 32 33
Code
Data
40 41 42 43 44 45 46 47 48 49 4A 4B 4C 4D 4E 4F 50 51 52 53
Code
Data
60 61 62 63 64 65 66 67 68 69 6A 6B 6C 6D 6E 6F 70 71
Code
-+00-+ 0-+-+0 0-+0-+ 0-++0-+0+0+0--+0 +0-0-+ +0-+0-+00+0-++-0 0-+0+0-+-0+ -+0-0+ +0-+-0 +0-0++0--0+ 0--+0+ -0-0++ -0-+0+ -0-++0
-++-00 +00+--+0-++ +-0-++ +-0+00 -+0+00 +00-00 -+++-0++-0+0+0-+0+-0+0+--0 0++--0 ++00-++0-0++0--0 +-00-+ 0+--+0 0+-0-+ 0+-+0-
-00+0+ 0-00++ 0-0+0+ 0-0++0 -00++0 00-0++ 00-+0+ 00-++0 00+000 ++-000 +-+000 -++000 0+-000 +0-000 0-+000 -0+000 +--+0+ -+-0++ -+-+0+ -+-++0
0++0-0 +0+-00 +0+0-0 +0+000++00++0-00 ++00-0 ++0000++-++0++-+0+-++0+--+ 0++--+ ++0+-++0-+++0--+ 000++000+-+ 000-++ 000+00
04 05 06
08 09 OA OB OC OD OE OF
APPENDIX D
8B/6T CODE
Table DI 8B/6T code (continued)
Data Code Data Code Data Code Data Code
14 15 16
0--++0 --00++ --0+0+ --0++0 -+0-+0 +-0-+0 -++-+0 +00-+0 +00+-0 -+++-0 +-0+-0 -+0+-0
34 35 36 37 38 39 3A 3B 3C 30 3E 3F AO Al A2 A3 A4 A5 A6 A7 A8 A9 AA
+-0+0-0+-+0 -0+0-+ -0++0+-00+0+-+-0 0+-0+0+--0+ +-0-0+ -0++-0 -0+0+-0+-0+
54 55 56 57 58 59 5A 5B 5C 50 5E 5F CO Cl C2 C3 C4 C5 C6 C7 C8 C9 CA CB CC CD CE CF DO 01 02 D3 D4
+--++0 --+0++ --++0+ --+++0 --0+++ -0-+++ 0--+++ 0--0++ +--0++ -000++ 0+++-0++-00
74 75 76
000+0000+-0 000-0+ 000-+0 +++--0 +++-0+++0- 0++0- -00-++ -00+00 +- --++ +- -+00
18 19 lA IB lC ID IE IF 80 81 82 83 84 85 86 87 88 89 8A 8B 8C 80 8E 8F 90 91
79 7A 7B 7C 7D 7E 7F EO El E2 E3 E4 E5 E6 E7 E8 E9 EA EB EC ED EE EF FO Fl F2 F3 F4
93 94
-00+-+ 0-0-++ 0-0+-+ 0-0++-00++00--++ 00-+-+ 00-++-000+0 0-0+00 0-00+0 0-000+ -0000+ 00-+00 00-0+0 00-00+ +--+-+ -+--++ -+-+-+ -+-+++--++-
-++0-0 +-+-00 +-+0-0 +-+00-++00++--00 ++-0-0 ++-00-++-++-++-+-+-++-+--+ -++--+ ++-+-++--+++---+ +000-0 0+0-00 0+00-0 0+000+0000-
AD AE AF
BO Bl B2 B3 B4
-+0+-+ 0-+-++ 0-++-+ 0-+++-+0+++0--++ +0-+-+ +0-++-+00+0 0-++00 0-+0+0 0-+00+ -+000+ +0-+00 +0-0+0 +0-00+ +-0+-+ 0+--++ 0+-+-+ 0+-+++-0++-
-++0-+ +-++0 +-+0-+ +-++0-+++0++--+0 ++-0-+ ++-+0-++0++-++-0 +-+0++-+-0+ -++-0+ ++-+-0 ++-0+++--0+ +000-+ 0+0-+0 0+00-+ 0+0+0+00+0-
APPENDIX D
8B/6T CODE
Table DI 8B/6Tcode (continued)
Data Code Data Code Data Code Data Code
95 96 97 98 99 9A 9B 9C 90 9E 9F
--+-++ --++-+ --++++--0+0 -+-+00 -+-0+0 -+-00+ +--00+ --++00 --+0+0 --+00+
B5 B6 B7 B8 B9 BA
BC BO BE BF
00+-00 00+0-0 00+00+00-+0+0+-0+0-+0+0--+ +00--+ 00++-00+-+00+--+
05 06 07 08 09 OA OB OC 00 OE OF
-0+-++ -0++-+ -0++++-00+0 0+-+00 0+-0+0 0+-00+ +-000+ -0++00 -0+0+0 -0+00+
F5 F6
F8 F9 FA FB FC
00+-+0 00+0-+ 00++0+000+0+0+-0 0+00+0+0-0+ +00-0+ 00++-0 00+0+00+-0+
APPENDIXE
Telephone History
In 9, we discussed telephone networks In this appendix, we briefly review the history of telephone networks The history in the United States can be divided into three eras: prior to 1984, between 1984 and 1996, and after 1996
Copyright © OnBarcode.com . All rights reserved.