Engineering Fundamentals: An Introduction to Engineering, 4th ed.c

604 Chapter 18 Mathematics in Engineering

of 50 C. To determine the time that it takes for a plate to reach a temperature of 50 C, we will

use the following logarithmic equation.

But what is meant by a logarithmic function? The logarithmic functions are defined for the

ease of computations. For example, if we let 10

x

y, then we define logyx. The symbol “log”

reads logarithm to the base-10 or common logarithm. For example, you know any number

raised to the power of zero has a value of 1 (that is 10

0

1); then using the definition of the

common logarithm, then log 1  0, for 10

1

 10, then log 10  1, for 10

2



100, then log 100 2, and so on. On the other hand, if we lete

x

y, then we define

ln yx, and the symbollnreads the logarithm to the base-e(or natural logarithm). More-

over, the relationship between the natural logarithm and the common logarithm is given by

12650 sec3.5 hr

t

rcL

2 h

ln

TiTf

TTf



1 7800 kg/m

3

21 400 J/kg#K 21 0.05 m 2

1221 25 W/m#K 2

ln

900  35

50  35

1.0

0.8

0.6

0.4

0.2

0.0

2.7 2.0 1.3 0.6 0.1 0.8 1.5 2.2

2 x

2

e x

2

f(x)

x

xy 2

x^2

e

x^2

2.6 0.009 0.001

2.4 0.018 0.003

2.2 0.035 0.008

 2 0.063 0.018

1.8 0.106 0.039

1.6 0.170 0.077

1.4 0.257 0.141

1.2 0.369 0.237

 1 0.500 0.368

0.8 0.642 0.527

0.6 0.779 0.698

0.4 0.895 0.852

0.2 0.973 0.961

0 1.000 1.000

0.2 0.973 0.961

0.4 0.895 0.852

0.6 0.779 0.698

0.8 0.642 0.527

1 0.500 0.368

1.2 0.369 0.237

1.4 0.257 0.141

1.6 0.170 0.077

1.8 0.106 0.039

2 0.063 0.018

2.2 0.035 0.008

2.4 0.018 0.003

2.6 0.009 0.001

■Figure 18.14 The plot off(x)  2

x^2

andf(x) e

x^2

.

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