Stitz-Zeager_College_Algebra_e-book

# 1 64 logarithmic equations and inequalities 373

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Unformatted text preview: 23 , so we get 4 log2 (x) + 3 = log2 x4 + 3 = log2 x4 + log2 23 Power Rule Since 3 = log2 23 = log2 x4 + log2 (8) = log2 8x4 2 The authors relish the irony involved in writing what follows. Product Rule 352 Exponential and Logarithmic Functions 4. To get started with − ln(x) − 1 , we rewrite − ln(x) as (−1) ln(x). We can then use the Power 2 1 Rule to obtain (−1) ln(x) = ln x−1 . In order to use the Quotient Rule, we need to write 2 √ 1 as a natural logarithm. Theorem 6.3 gives us 2 = ln e1/2 = ln ( e). We have − ln(x) − 1 2 1 2 = (−1) ln(x) − = ln x−1 − = ln x−1 1 2 Power Rule e1/2 − ln √ = ln x−1 − ln ( e) = ln = ln x−1 √ e 1 √ xe Since 1 2 = ln e1/2 Quotient Rule As we would expect, the rule of thumb for re-assembling logarithms is the opposite of what it was for dismantling them. That is, if we are interested in rewriting an expression as a single logarithm, we apply log properties following the usual order of operations: deal with multiples of...
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