h power and from that result we take the qth root. These calculations are particularly easy to do with a scientific calculator as the X function, where y can even be a decimal like -3.7. B.3.3 Simple Linear Algebraic Equations An equation is a statement of equality between two expressions. Equations are of two types: identities and conditional equations (or usually simply equations). A conditional equation is true only for certain values of the variables involved; for example, X + 2 = 5 is a true statement only when X = 3; and xy + y - 3 = 0 is true when X = 2 and y = 1, and for many other pairs of values of X and y; but for still others it is false. Equation (9.20) in the text is an identity. It states that G/T = G - 10 log T, where G is gain and T is noise temperature. Actually the right-hand side of the equation is just a restatement of the left-hand side; it doesn't tell us anything new. In many cases, identities, such as this one, are very useful in analysis. There are various rules for equations. An equation has a right-hand side and a left-hand side. Maintaining equality is paramount. For example, if we add some value to the left side, we must add the same value to the right side. Likewise, if we divide the (entire) left side by a value, we must divide the (entire) right by the same value. As we might imagine, we must carry out similar procedures for subtraction and multiplication. A linear equation is of the following form: Ax + B = 0 (A # 0). This is an equation with one unknown, X. A will be a fixed quantity, a number; SO will B. However, in the parentheses it states that A may not be 0. Let's practice with some examples. In each case calculate the value of X. + 5 = 7. A REVIEW OF MATHEMATICS FOR TELECOMMUNICATION APPLICATIONS Clue: We want to have X alone on the left side. To do this we subtract 5 from the left side, but following the rules, we must also subtract 5 from the right side. Thus, X + 5 - 5 7-5 or X ==2. Another example is 3X+7= 31. Again, we want X alone. But first we must settle for 3X. Su