College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 6 - Section 6.5 - Properties of Logarithms - 6.5 Assess Your Understanding - Page 460: 94

Answer

$y=Ce^{5x}-4$

Work Step by Step

Subtract by $\ln{C}$ on both sides: $\ln{(y+4)} - \ln{C}=5x$ RECALL: For positive real numbers M and N: $\ln{M} - \ln{N} = \ln{\left(\dfrac{M}{N}\right)}$ Use the rule above to obtain: $\ln{\left(\dfrac{y+4}{C}\right)}=5x$ RECALL: $\ln{M}= y \longrightarrow e^y=M$ Use the rule above to obtain: $e^{5x}=\dfrac{y+4}{C}$ Multiply by $C$ on both sides of the equation to obtain: $C \cdot e^{5x} = C \cdot \dfrac{y+4}{C} \\Ce^{5x} = y+4 \\y+4=Ce^{5x}$ Subtract by $4$ on both sides of the equation to obtain: $y+4-4 = Ce^{5x}-4 \\y=Ce^{5x}-4$
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