Unformatted text preview: g(x) + 2 log(y ) − log(z ) 4. − ln(x) − 1
2 Solution. Whereas in Example 6.2.1 we read the properties in Theorem 6.6 from left to right to
expand logarithms, in this example we read them from right to left.
1. The diﬀerence of logarithms requires the Quotient Rule: log3 (x − 1) − log3 (x +1) = log3 x− 1
x+1 . 2. In the expression, log(x) + 2 log(y ) − log(z ), we have both a sum and diﬀerence of logarithms.
However, before we use the product rule to combine log(x) + 2 log(y ), we note that we need
to somehow deal with the coeﬃcient 2 on log(y ). This can be handled using the Power Rule.
We can then apply the Product and Quotient Rules as we move from left to right. Putting it
all together, we have
log(x) + 2 log(y ) − log(z ) = log(x) + log y 2 − log(z )
= log xy 2 − log(z )
z Power Rule
Quotient Rule 3. We can certainly get started rewriting 4 log2 (x) + 3 by applying the Power Rule to 4 log2 (x)
to obtain log2 x4 , but in order to use the Product Rule to handle the addition, we need to
rewrite 3 as a logarithm base 2. From Theorem 6.3, we know 3 = log2...
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