nent-the exponent to which the base is raised to yield the number. The expression loga y is read: "logarithm of y to the base a." The two equations ax = y and loga y = X are two different ways of expressing the relationship between the numbers X, y, and a. The first equation is in the exponential form, and the second is in the logarithmic form. Thus 26 = 64 is equivalent to log2 64 = 6. Likewise, the statement log16(1/4) = - 1/2 implies 16-1/2 = 1/4. These concepts should be thoroughly understood before proceeding. B.4.2 Laws of Logarithms In Section B.3 we discussed the laws of adding and subtracting exponents. From these laws we can derive the laws of logarithms. Let's say that the generalized base of a logarithm is a, which is positive, and that X and y are real numbers. Here we mean they are not imaginary numbers (i.e., based one the square root of -1). Note that a can be any positive number. However, we concentrate on a = 10-that is, on logarithms to the base 10. The scientific calculator should be used to obtain the logarithm by using the "log" button. There will also probably be an "In" button. This button is used to obtain logarithms to the natural base, where a = 2.71828183+. Law 1. The logarithm of the product of two numbers equals the sum of the logarithms of the factors. That is, loga xy = loga X + loga y. Law 2. The logarithm of the quotient of two numbers equals the logarithm of the dividend minus the logarithm of the divisor. That is, ga x/y=logax-loga Law 3. The logarithm of the nth power of a number equals n times the logarithm of the number. That is, Table B.1 Selected Powers of Ten Power Logarithm of Value of of 10 Number Number Logarithm 10,000 log10,000 log1000 log100 log10 log0.1 -1 or 9 - 10 log0.01 -2 or 8 - 10 0.001 log0.001 -3 or 7 - 10 0.0001 log0.0001 -4 or 6 - 10 B.4 LOGARITHMS TO THE BASE 10 Law 4. The logarithm of the pth root of a number is equal to the logarithm of the number divided by p. That is, Remember that if X = 1, loga X = 0. Here is an exercise. Express log 10(38)1/2(60)/