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: 12

Answer

a.) $5^{-3} = \frac{1}{125}$ b.) $8^{\frac{2}{3}} = 4$

Work Step by Step

$Express$ $the$ $equation$ $in$ $exponential$ $form:$ a.) $\log_5 (\frac{1}{125}) = -3$ b.) $\log_8 4 = \frac{2}{3}$ Logarithmic form to exponential form: $\log_b a = c \rightarrow b^c = a$ a.) $\log_5 (\frac{1}{125}) = -3$ Plug in 5 for b, $\frac{1}{125}$ for a, and -3 for c $\log_5 (\frac{1}{125}) = -3 \rightarrow 5^{-3} = \frac{1}{125}$ b.) $\log_8 4 = \frac{2}{3}$ Plug in 8 for b, 4 for a, and $\frac{2}{3}$ for c $\log_8 4 = \frac{2}{3} \rightarrow 8^{\frac{2}{3}} = 4$
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