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Unformatted text preview: e called ‘logs’ for short.
Definition 6.2. The inverse of the exponential function f (x) = bx is called the base b logarithm
function, and is denoted f −1 (x) = logb (x) The expression logb (x) is read ‘log base b of x.’
We have special notations for the common base, b = 10, and the natural base, b = e.
Definition 6.3. The common logarithm of a real number x is log10 (x) and is usually written
log(x). The natural logarithm of a real number x is loge (x) and is usually written ln(x).
Since logs are deﬁned as the inverses of exponential functions, we can use Theorems 5.2 and 5.3 to
tell us about logarithmic functions. For example, we know that the domain of a log function is the
range of an exponential function, namely (0, ∞), and that the range of a log function is the domain
of an exponential function, namely (−∞, ∞). Since we know the basic shapes of y = f (x) = bx for
the diﬀerent cases of b, we can obtain the graph of y = f −1 (x) = logb (x) by reﬂecting the graph of
f across the line y = x...
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