By Mark Ball
This available textual content brings jointly mathematical suggestions that may be fundamental to each pupil, instructor, practitioner, and person of chemistry- or biology-related laboratory paintings. Responding to the troubles of either teachers and scholars, CLINICAL LABORATORY MATHEMATICS starts with a assessment of mathematics and algebra. subsequent, it offers example-rich chapters on exponential notation and logarithms, rounding and determine value, dimension platforms, ideas and concentrations, dilutions, proportionality, graphs, charges of swap, facts, chemistry, quality controls, and strategy evaluate. It solutions commonly asked questions, identifies universal misunderstandings, and gives an not obligatory complex part on-line. all through, the writer explains why a great figuring out of math is necessary in present day high-technology medical laboratories. perform difficulties are strategically designed to provide real-world situations with either context and end result. helping either self-guided research and conventional lecture-discussion, the textual content is logically equipped and liberally cross-referenced, revealing hidden connections and customary motifs.
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If the base-10 logarithm of x is q, then what is the natural logarithm of x? If the natural logarithm of x is w, then what is the base-10 logarithm of x? 303q 2. 3. 303 The Usefulness of Logarithms Clearly, logarithms have properties that make them quite useful in science and technology—properties that explain the importance of logarithms in the situations listed in the introduction to this chapter. At this point, let us summarize the reasons for laboratory professionals to develop a working understanding of logarithms.
Then, append “ * 10-b,” where b is the number of places you moved the decimal. 10. There are algebraic rules for simplifying various calculations that involve exponents and logarithms. These equations are particularly handy for manipulating fractional exponents. 11. An arithmetic scale is one in which equal distances between tick marks represent equal amounts. The distance between any two adjacent tick marks is the same as the distance between any other two adjacent tick marks. A logarithmic scale is one in which equal distances between tick marks represent not equal amounts, but equal ratios.
The judicious use of logarithmic scales or of logarithms can solve this problem. 01 Each value on this axis is the logarithm of the corresponding value on the other axis. n Figure 2-3 The y-axes of Figures 2-2A and 2-2B are juxtaposed to show c orrespondence between their scales. Each pink double-headed arrow links a number on the logarithmic scale (the scale on the right) to its logarithm on the arithmetic scale (the scale on the left). 43 4500 4000 3500 3000 2500 2000 1500 1000 500 0 10000 A Bacterial cells per mL Bacterial cells per mL Chapter 2 • Exponential Notation and Logarithms B 1000 100 10 1 0 1 2 3 0 4 1 2 3 4 Incubation time (h) Incubation time (h) Inoculation n Figure 2-4 Growth data for a culture of E.