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domains, and, hence, are diﬀerent functions. We leave it to the reader to verify the domain of f
is (−∞, −2) ∪ (2, ∞) whereas the domain of g is (2, ∞). In general, when using log properties to
1 At this point in the text, the reader is encouraged to carefully read through each step and think of which quantity
is playing the role of u and which is playing the role of w as we apply each property. 6.2 Properties of Logarithms 351 expand a logarithm, we may very well be restricting the domain as we do so. One last comment
before we move to reassembling logs from their various bits and pieces. The authors are well aware
of the propensity for some students to become overexcited and invent their own properties of logs
like log117 x2 − 4 = log117 x2 − log117 (4), which simply isn’t true, in general. The unwritten2
property of logarithms is that if it isn’t written in a textbook, it probably isn’t true.
Example 6.2.2. Use the properties of logarithms to write the following as a single logarithm.
1. log3 (x − 1) − log3 (x + 1) 3. 4 log2 (x) + 3 2. lo...

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