College Algebra (10th Edition)

Published by Pearson

Chapter 6 - Section 6.5 - Properties of Logarithms - 6.5 Assess Your Understanding: 87

Answer

$y=Cx$

Work Step by Step

RECALL: For positive real numbers M and N: (1) $\ln{M} = \ln{N} \longrightarrow M=N$ (2) Product Rule: $\ln{M} + \ln{N} = \ln{(MN)}$ (3) Quotient Rule: $\ln{M} - \ln{N} = \ln{\left(\dfrac{M}{N}\right)}$ (4) Power Rule: $r\cdot ln {M} = \ln{(M^r)}$ Use the Product Rule to obtain: $\ln{y}=\ln{x}+\ln{C} \\\ln{y}=\ln{[x(C)]} \\\ln{y}=\ln{(Cx)}$ Use rule (1) in above to obtain: $\ln{y}=\ln{(Cx)} \longrightarrow y=Cx$ Thus, $y=Cx$

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