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The logical operators are shown next:

The expression equals log3 ( 34 ) 5 log2 ( 23 ) 3 ln e4 = 4 log3 3 5 3 log2 2 3 4 ln e = 4 1 5 3 1 3 4 1 = 23

The outcome of the relational and logical operators is a bool value In general, objects can be compared for equality or inequality using == and != However, the comparison operators, <, >, <=, or >=, can be applied only to those types that support an ordering relationship Therefore, all of the relational operators can be applied to all numeric types However, values of type bool can only be compared for equality or inequality since the true and false values are not ordered For example, true > false has no meaning in C#

Part I:

For the logical operators, the operands must be of type bool, and the result of a logical operation is of type bool The logical operators, &, |, ^, and !, support the basic logical operations AND, OR, XOR, and NOT, according to the following truth table:

As the leader in the silk ower industry, we create arrangements that are lush and full and always custom designed All arrangements feature seasonal blossoms in an array of colors to create just the look you seek Our owers will be perfect, whether the occasion is a wedding, reunion, business meeting or conference, or other event We guarantee that every arrangement will be custom designed to your speci cations, delivered on time, and at or below budget (Four sentences totaling seventy-six words [20 + 17 + 19 + 20 = 76] average nineteen words per sentence)

Applying the rules for logarithms we obtain ln( 5x ) + ln( 23x ) = ln 4 ln( 7x ) or x ln 5 + 3x ln 2 = ln 4 x ln 7

p False True False True q False False True True p&q False False False True p|q False True True True p^q False True True False !p True False True False

As the table shows, the outcome of an exclusive OR operation is true when one and only one operand is true Here is a program that demonstrates several of the relational and logical operators:

// Demonstrate the relational and logical operators using System; class RelLogOps { static void Main() { int i, j; bool b1, b2; i = 10; j = 11; if(i < j) ConsoleWriteLine("i < j"); if(i <= j) ConsoleWriteLine("i <= j"); if(i != j) ConsoleWriteLine("i != j"); if(i == j) ConsoleWriteLine("this won't execute"); if(i >= j) ConsoleWriteLine("this won't execute"); if(i > j) ConsoleWriteLine("this won't execute"); b1 = true; b2 = false; if(b1 & b2) ConsoleWriteLine("this won't execute"); if(!(b1 & b2)) ConsoleWriteLine("!(b1 & b2) is true"); if(b1 | b2) ConsoleWriteLine("b1 | b2 is true"); if(b1 ^ b2) ConsoleWriteLine("b1 ^ b2 is true"); } }

The output from the program is shown here:

Gathering together all the terms involving x yields x [ln 5 + 3 ln 2 + ln 7] = ln 4 or x [ln( 5 23 7) ] = ln 4 Solving for x gives x= ln 4 = log280 4 ln 280

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