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 - Mid-Chapter Check Point - Page 715: 24


evaluation is not possible

Work Step by Step

Note that $8=2^3$. Thus, the given expression is equivalent to: $=\log_3{(\log_2{(\frac{1}{2^3})})}$ Use the rule $\dfrac{1}{a^m} = a^{-m}$ to obtain: $=\log_3{(\log_2{(2^{-3})})}$ RECALL: $\log_b{b^x} = x$ Use the rule above to obtain: $=\log_3{(-3)}$ Note that the logarithmic function is defined as: $y=\log_b{x} \longrightarrow b^y=x$ where $x \gt 0$ The expression above has $x=-3$. Since logarithms are only defined when $x \gt 0$, then the given expression cannot be evaluated.
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