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: 41

Answer

$92$

Work Step by Step

Note that $16=2^4$. Thus, the given expression is equivalent to: $=\log_2{[(2^4)^{23}]}$ Using the rule $(a^m)^n=a^{mn}$, the expression above simplifies to: $=\log_2{(2^{4\cdot 23})} \\=\log_2{(2^{92})}$ RECALL: $\log_a{(a^k)} = k$ Use the rule above to obtain: $\log_2{(2^{92})} = 92$
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