Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 4 - Section 4.3 - Logarithmic Functions - 4.3 Exercises - Page 351: 8

Answer

$\underline{4^3=64}$ $log_4{64}=3$ -- $log_4{2}=\frac{1}{2}$ $\underline{4^{\frac{1}{2}}=2}$ -- $\underline{4^{\frac{3}{2}}=8}$ $\log_4{8}=\frac{3}{2}$ -- $log_4{\frac{1}{16}}=-2$ $\underline{4^{-2}=\frac{1}{16}}$ -- $log_4{\frac{1}{2}}=-\frac{1}{2}$ $\underline{4^{-\frac{1}{2}}=\frac{1}{2}}$ -- $\underline{4^{-\frac{5}{2}}=\frac{1}{32}}$ $\log_4{\frac{1}{32}}=-\frac{5}{2}$

Work Step by Step

Before we begin, let's shortly overview what is logarithmic expression. $\log_a{x}=b$ this is a logarithmic form which by exponential form means $a^b=x$. According to this we can easily fill the table. --- $4^3=64$ This is similar to: $log_4{64}=3$ $log_4{2}=\frac{1}{2}$ This one is same as: $4^{\frac{1}{2}}=2$ $4^{\frac{3}{2}}=8$ It's equal to: $\log_4{8}=\frac{3}{2}$ $log_4{\frac{1}{16}}=-2$ It's similar to: $4^{-2}=\frac{1}{16}$ $log_4{\frac{1}{2}}=-\frac{1}{2}$ It's similar to: $4^{-\frac{1}{2}}=\frac{1}{2}$ $4^{-\frac{5}{2}}=\frac{1}{32}$ It's similar to: $\log_4{\frac{1}{32}}=-\frac{5}{2}$
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