Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 9 - Section 9.3 - Logarithmic Functions - Exercise Set: 79

Answer

$2$

Work Step by Step

RECALL: (i) $\log_b{b} = 1$ (ii) $\log_b{1}=0$ (iii) $\log_b{b^x} = x$ Write $81$ as $3^4$ to obtain: $=\log_2{(\log_3{3^4})}$ With $b=3$ and $x=4$, use rule (iii) to obtain: $\log_2{(\log_3{3^4})}=\log_2{4}$ Write $4$ as $2^2$ to obtain: $=\log_2{2^2}$ Use rule (iii) above to obtain: $\log_2{2^2}=2$
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