Common Mathematical Operations In Chemistry Worksheets With Answers
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14Appendix A
A-1
3.2 Section
•
Determining the Formula of an Unknown Compound
Common Mathematical
Operations in Chemistry
I
n addition to basic arithmetic and algebra, four mathematical operations are used
frequently in general chemistry: manipulating logarithms, using exponential nota-
tion, solving quadratic equations, and graphing data. Each is discussed briefly
below.
ManIpUlatIng logarIthMs
Meaning and Properties of Logarithms
A logarithm is an exponent. Specifically, if x
n
A, we can say that the logarithm to
the base x of the number A is n, and we can denote it as
log
A n
x
Because logarithms are exponents, they have the following properties:
log
1 0
x
log
(A 3 B) log
A 1 log
B
x
x
x
A
log
5 log
A 2 log
B
x
x
x
B
log
A
y
y log
A
x
x
Types of Logarithms
Common and natural logarithms are used in chemistry and the other sciences.
1. For common logarithms, the base (x in the examples above) is 10, but they are
written without specifying the base; that is, log
A is written more simply as log A;
10
thus, the notation log means base 10. The common logarithm of 1000 is 3; in other
words, you must raise 10 to the 3rd power to obtain 1000:
log 1000 3
or
10
3
1000
Similarly, we have
log 10 1
or
10
1
10
6
log 1,000,000 6
or
10
1,000,000
log 0.001 23
or
10
0.001
23
log 853 2.931
or
10
2.931
853
The last example illustrates an important point about significant figures with all loga-
rithms: the number of significant figures in the number equals the number of digits to
the right of the decimal point in the logarithm. That is, the number 853 has three
significant figures, and the logarithm 2.931 has three digits to the right of the decimal
point.
To find a common logarithm with an electronic calculator, enter the number and
press the log button.
2. For natural logarithms, the base is the number e, which is 2.71828 . . . , and
log
A is written ln A; thus, the notation ln means base e. The relationship between
e
the common and natural logarithms is easily obtained:
log 10 1
and
ln 10 2.303
A-1
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