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: 22

Answer

a.) $\log_3 10 = 2x$ b.) $\log 0.1 = -4x$

Work Step by Step

$Express$ $the$ $equation$ $in$ $logarithmic$ $form:$ a.) $3^{2x} = 10$ b.) $10^{-4x} = 0.1$ Exponential form to logarithmic form: $b^c = a \rightarrow \log_b a = c$ a.) $3^{2x} = 10$ Plug in 3 for b, 2x for c, and 10 for a $3^{2x} = 10 \rightarrow \log_3 10 = 2x$ b.) $10^{-4x} = 0.1$ Plug in 10 for b, -4x for c, and 0.1 for a $10^{-4x} = 0.1 \rightarrow \log_10 0.1 = -4x \rightarrow \log 0.1 = -4x$
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