College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 4, Exponential and Logarithmic Functions - Chapter 4 Review - Concept Check: 35

Answer

$-3$

Work Step by Step

Note that $27=3^3$. Thus, $\log_3{(\frac{1}{27})}=\log_3{(\frac{1}{3^3})}$ Use the rule $\dfrac{1}{a^m} = a^{-m}$ to obtain: $\log_3{(\frac{1}{3^3})} = \log_3{(3^{-3})}$ RECALL: $\log_a{(a^n)} = n$ Use the rule above to obtain: $\log_3{(3^{-3})} = -3$
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