College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 4 - Exponential and Logarithmic Functions - Exercise Set 4.3: 96

Answer

False, $\ln x+\ln(2x)= \ln(2x^{2})$ or $\ln 3+\ln x$=$\ln(3x)$

Work Step by Step

Applying The Product Rule: $\log_{\mathrm{b}}(\mathrm{M}\mathrm{N})=\log_{\mathrm{b}}\mathrm{M}+\log_{\mathrm{b}}\mathrm{N}$, to the LHS we should have $\ln x+\ln(2x)=\ln(x\cdot 2x)=\ln(2x^{2}),$ which is differrent to the problem statement's RHS. So, the problem statement is false. To make it true, change the RHS to $\ln(2x^{2}),$ ------------------ Alternatively, we could have started from the RHS, applying the Product Rule: $\ln(3\cdot x)=\ln 3+\ln x,$ so the statement becomes true if you change the LHS to $\ln 3+\ln x$.
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