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: 94

Answer

False, $\ln(x\cdot 1)=\ln x+\ln 1$

Work Step by Step

On the RHS, the term ln1 equals zero, (a basic logarithmic property, so the equation of the problem statement is equivalent to ln(x+1)=lnx, which is false. A property for expanding $\log_{b}(...sum...)$ does not exist. There is, however, The Product Rule: $\log_{\mathrm{b}}(\mathrm{M}\mathrm{N})=\log_{\mathrm{b}}\mathrm{M}+\log_{\mathrm{b}}\mathrm{N}$ which has the same form of the RHS as the problem statement. Therefore, a change making the statement true would be: $\ln(x\cdot 1)=\ln x+\ln 1$
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