Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 3 - Section 3.2 - Exponential Functions - Exercise Set: 107

Answer

$2$

Work Step by Step

RECALL: (i) $\log_b{b}=1.$ (ii) $\log_b{b^x}=x.$ (iii) $\log_b{1} = 0.$ Note that $81=3^4$. Thus, the given expression can be written as $\log_2{(\log_3{3^4})}.$ Use rule (ii) above to obtain $\log_2{(\log_3{3^4})}=\log_2{4} = \log_2{2^2}.$ Use rule (ii) above to obtain $\log_2{2^2} =2.$
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