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: 36

Answer

$t = -16.2$

Work Step by Step

$\log_3 (-5t) + 13 = 17$ $\log_3 (-5t) = 17 - 13$ $\log_3 (-5t) = 4$ $3^{4} = -5t$ $81 = -5t$ $t = -\frac{81}{5}$ $t = -16.2$ Check: $\log_3 (-5(-16.2)) + 13 \overset{?}{=} 17$ $\log_3 (81) + 13 \overset{?}{=} 17$ $\log_3 (3^{4}) + 13 \overset{?}{=} 17$ $4\log_3 (3) + 13 \overset{?}{=} 17$ $4(1) + 13 \overset{?}{=} 17$ $4+ 13 \overset{?}{=} 17$ $17 = 17$
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