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Logarithms and Exponentials 369
10 0.5 ≈ 0.3162
10 1 0.1
10 1.7 ≈ 0.01995
10 2 0.01
In the first equation, 2 is the argument, or value on which the exponential function
depends, and 100 is the resultant. You would say, “The common exponential of 2 is
equal to 100.” In the second equation, you would say, “The common exponential of
1.478 is approximately 30.06.” As with logarithms, the arguments in an exponential
function need not be whole numbers. They can even be irrational; you could speak of
10 , for example. It happens to be approximately equal to 1,385.
Figure 24-5 is a partial linear coordinate graph of the function y 10 x . Figure 24-6 is
a partial graph of the same function in semilog coordinates. The domain of the common
exponential function encompasses the entire set of real numbers. The range is limited
to the positive real numbers. This reflects the fact that you can never raise a real number
to any real power and get a negative number.
NATURAL EXPONENTIALS
Base-e exponentials are also known as natural exponentials. Here are some examples,
using the same arguments as in the previous section:
e 2 ≈ 7.389
e 1.478 ≈ 4.384
e 1 ≈ 2.718
Figure 24-5
Partial linearcoordinate
graph
of the common
exponential function.
As x becomes
arbitrarily large in
the negative
sense, the value of
y approaches 0.
As x increases
without limit, so
does y.