Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 4 - Review - Exercises: 41



Work Step by Step

$Evaluate$ $the$ $expression$ $without$ $using$ $a$ $calculator:$ $\log_2 16^{23}$ Use the Third Law of Logarithms: $\log x^a = a\log x$ $$\log_2 16^{23} = 23\log_2 16$$ Rewrite 16 as $2^4$ $$23\log_2 2^4$$ Use the Third Property of Logarithms: $\log_a a^x = x$ $$23\log_2 2^4 = 23\times4 = 92$$
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