Intermediate Algebra: Connecting Concepts through Application

Published by Brooks Cole
ISBN 10: 0-53449-636-9
ISBN 13: 978-0-53449-636-4

Chapter 6 - Logarithmic Functions - Chapter Review Exercises: 49

Answer

$t = \frac{1}{4.3e^{4.5}}$

Work Step by Step

$\ln (4.3t) + 7.5 = 3$ $\ln 4.3t = -4.5$ $4.3t = e^{-4.5}$ $4.3t = \frac{1}{e^{4.5}}$ $t = \frac{1}{e^{4.5}}(\frac{1}{4.3})$ $t = \frac{1}{4.3e^{4.5}}$ Check: $\ln (4.3t) + 7.5 \overset{?}{=} 3$ $\ln (4.3(\frac{1}{4.3e^{4.5}})) + 7.5 \overset{?}{=} 3$ $\ln (\frac{1}{e^{4.5}}) + 7.5 \overset{?}{=} 3$ $\ln (e^{-4.5}) \overset{?}{=} -4.5$ $-4.5 = -4.5$
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