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 - 6.6 Solving Logarithmic Equations - 6.6 Exercises: 66

Answer

$x = \frac{1}{e^{2}}$

Work Step by Step

$\ln x + 7 = 5$ $\ln x = 5 - 7$ $\ln x = -2$ $x = e^{-2}$ $x = \frac{1}{e^{2}}$ Check: $\ln x + 7 \overset{?}{=} 5$ $\ln e^{-2} + 7 \overset{?}{=} 5$ $-2\ln e + 7 \overset{?}{=} 5$ $-2(1) + 7 \overset{?}{=} 5$ $-2 + 7 \overset{?}{=} 5$ $5 = 5$
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