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Stitz-Zeager_College_Algebra_e-book

64 logarithmic equations and inequalities 1 1 1 lnx

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Unformatted text preview: + 2) + log117 (x − 2) Product Rule A couple of remarks about Example 6.2.1 are in order. First, while not explicitly stated in the above example, a general rule of thumb to determine which log property to apply ﬁrst to a complicated problem is ‘reverse order of operations.’ For example, if we were to substitute a number for x into the expression log0.1 10x2 , we would ﬁrst square the x, then multiply by 10. The last step is the multiplication, which tells us the ﬁrst log property to apply is the Product Rule. In a multi-step problem, this rule can give the required guidance on which log property to apply at each step. The reader is encouraged to look through the solutions to Example 6.2.1 to see this rule in action. Second, while we were instructed to assume when necessary that all quantities represented positive real numbers, the authors would be committing a sin of omission if we failed to point out that, for instance, the functions f (x) = log117 x2 − 4 and g (x) = log117 (x + 2) + log117 (x − 2) have diﬀer...
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