Part C Logarithms

Sections 17.9 and 17.10 are the only places in this text that use logarithms, and most of what you need to know about logarithms is explained at that point. Comments here are limited to basic information needed to support the text explanations. 

The common logarithm of a number is the power, or exponent, to which 10 must be raised to be equal to the number. Expressed mathematically. 

Because logarithms are exponents, they are governed by the rules of exponents given in Section 9 of Part B of this Appendix. For example, the product of two exponentials to the same base is the base raised to a power equal to the sum of the exponents a X a = a . The exponents are added. Similarly, exponents to the base 10 (logarithms) are added to get the logarithm of the product of two numbers 10 X 10 = 10 4 . Thus 

In a similar fashion, the logarithm of a quotient is the logarithm of the dividend minus the logarithm of the divisor (or the logarithm of the numerator minus the logarithm of the denominator if the expression is written as a fraction)  

Equation AP.l is the basis for converting between pH and hydrogen ion concentration in Section 17.9—or between any p number and its corresponding value in exponential notation. This is the only application of logarithms in this text. In more advanced chemistry courses you will encounter applications of Equation AP.3 and others that are beyond the scope of this discussion. 

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