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 - Page 477: 97


False, $\displaystyle \log(x+3)-\log(2x)=\log(\frac{x+3}{2x})$

Work Step by Step

Applying the Quotient Rule: $\displaystyle \log_{\mathrm{b}}(\frac{\mathrm{M}}{\mathrm{N}})=\log_{\mathrm{b}}\mathrm{M}-\log_{\mathrm{b}}\mathrm{N}$, LHS=$\displaystyle \log(x+3)-\log(2x)=\log(\frac{x+3}{2x})$, which does not equal the RHS of the problem statement. (There is no rule to expand a quotient OF logarithms, which is what we have there) So, the statement is false. To make it true, change the RHS to $\displaystyle \log(\frac{x+3}{2x})$.
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