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: 19

Answer

a.) $\log_8 \frac{1}{8} = -1$ b.) $\log_2 \frac{1}{8} = -3$

Work Step by Step

$Express$ $the$ $equation$ $in$ $logarithmic$ $form:$ a.) $8^{-1} = \frac{1}{8}$ b.) $2^{-3} = \frac{1}{8}$ Exponential form to logarithmic form: $b^c = a \rightarrow \log_b a = c$ a.) $8^{-1} = \frac{1}{8}$ Plug in 8 for b, -1 for c, and $\frac{1}{8}$ for a $8^{-1} = \frac{1}{8} \rightarrow \log_8 \frac{1}{8} = -1$ b.) $2^{-3} = \frac{1}{8}$ Plug in 2 for b, -3 for c, and $\frac{1}{8}$ for a $2^{-3} = \frac{1}{8} \rightarrow \log_2 \frac{1}{8} = -3$
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