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Formatting is governed by two components: format specifiers and format providers The form that the string representation of a value will take is controlled through the use of a format specifier Thus, it is the format specifier that dictates how the human-readable form of the data will look For example, to output a numeric value using scientific notation, you will use the E format specifier In many cases, the precise format of a value will be affected by the culture and language in which the program is running For example, in the United States, money is represented in dollars In Europe, money is represented in euros To handle the cultural and language differences, C# uses format providers A format provider defines the way that a format specifier will be interpreted A format provider is created by implementing the IFormatProvider interface, which defines the GetFormat( ) method Format providers are predefined for the built-in numeric types and many other types in the NET Framework In general, you can format data without having to worry about specifying a format provider, and format providers are not examined further in this book To format data, include a format specifier in a call to a method that supports formatting The use of format specifiers was introduced in 3, but is worthwhile reviewing here The discussion that follows uses ConsoleWriteLine( ), but the same basic approach applies to other methods that support formatting To format data using WriteLine( ), use the version of WriteLine( ) shown here: WriteLine( format string , arg0, arg1, , argN); In this version, the arguments to WriteLine( ) are separated by commas and not + signs The format string contains two items: regular, printing characters that are displayed as-is, and format commands Format commands take this general form: {argnum, width: fmt} Here, argnum specifies the number of the argument (starting from zero) to display The minimum width of the field is specified by width, and the format specifier is represented by fmt Both width and fmt are optional Thus, in its simplest form, a format command simply indicates which argument to display For example, {0} indicates arg0, {1} specifies arg1, and so on During execution, when a format command is encountered in the format string, the corresponding argument, as specified by argnum, is substituted and displayed Thus, it is the position of a format specifier within the format string that determines where its matching data will be displayed It is the argument number that determines which argument will be formatted If fmt is present, then the data is displayed using the specified format Otherwise, the default format is used If width is present, then output is padded with spaces to ensure that the minimum field width is attained If width is positive, output is right-justified If width is negative, output is left-justified The remainder of this chapter examines formatting and format specifiers in detail.

boundary conditions x(0) = F1 and x (1) = Fr is expressed, not including boundary conditions, using Eq (525), as:

SOLUTION If x > 0 then ln x ln x = = ln x ln e 1 Thus we see that the natural logarithm ln x is precisely the same as loge x loge x = Math Note: In mathematics, it is common to write ln x rather than loge x You Try It: Calculate log3 27 + log5 (1/25) log2 8

Part II:

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There are several format specifiers defined for numeric data They are shown in Table 22-4 Each format specifier can include an optional precision specifier For example, to specify that a value be represented as a fixed-point value with two decimal places, use F2 As explained, the precise effect of certain format specifiers depends upon the cultural settings For example, the currency specifier, C, automatically displays a value in the monetary format of the selected culture For most users, the default cultural information matches their locale and language Thus, the same format specifier can be used without concern about the cultural context in which the program is executed Here is a program that demonstrates several of the numeric format specifiers:

(526)

// Demonstrate various format specifiers using System; class FormatDemo { static void Main() { double v = 1768865849; double v2 = 015; int x = 21; ConsoleWriteLine("{0:F2}", v); ConsoleWriteLine("{0:N5}", v); ConsoleWriteLine("{0:e}", v); ConsoleWriteLine("{0:r}", v); ConsoleWriteLine("{0:p}", v2); ConsoleWriteLine("{0:X}", x); ConsoleWriteLine("{0:D12}", x); ConsoleWriteLine("{0:C}", 18999); } }

The output is shown here:

We will be able to do calculations much more easily if we learn some simple properties of logarithms and exponentials If a > 0 and b > 0 then a (loga b) = b If a > 0 and b R is arbitrary then loga (a b ) = b If a > 0, b > 0, and c > 0 then (i) loga (b c) = loga b + loga c (ii) loga (b/c) = loga b loga c logc b (iii) loga b = logc a 1 (iv) loga b = logb a (v) loga 1 = 0 (vi) loga a = 1 (vii) For any exponent , loga (b ) = (loga b) We next give several examples to familiarize you with logarithmic and exponential operations EXAMPLE 621

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