Precalculus: Mathematics for Calculus, 7th Edition

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

Chapter 4 - Section 4.3 - Logarithmic Functions - 4.3 Exercises: 28

Answer

a.) 5 b.) 17 c.) 0

Work Step by Step

$Evaluate$ $the$ $expression:$ a.) $\log_2 32$ b.) $\log_8 8^{17}$ c.) $\log_6 1$ a.) $\log_2 32$ Rewrite 32 as $2^5$ [Note: $2^5 = 2\times2\times2\times2\times2 = 32$] $\log_2 2^5$ Use the Third Property of Logarithms: $\log_a a^x = x$ $\log_2 2^5 = 5$ b.) $\log_8 8^{17}$ Use the Third Property of Logarithms: $\log_a a^x = x$ $\log_8 8^{17} = 17$ c.) $\log_6 1$ Rewrite 1 as $6^0$ [Note: Any number or variable to the power of 0 equals 1] $\log_6 6^0$ Use the Third Property of Logarithms: $\log_a a^x = x$ $\log_6 6^0 = 0$
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