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: 98


False, $\displaystyle \log(\frac{x+2}{x-1}) = \log(x+2)-\log(x-1)$

Work Step by Step

The LHS is a quotient OF logarithms. No rule/property exists with which we can expand or simplify. The RHS is a diffeence of logarithms, which appears in the Quotient Rule (on its RHS): $\displaystyle \log_{\mathrm{b}}(\frac{\mathrm{M}}{\mathrm{N}})=\log_{\mathrm{b}}\mathrm{M}-\log_{\mathrm{b}}\mathrm{N}$, so statement RHS = $\displaystyle \log(x+2)-\log(x-1)=\log(\frac{x+2}{x-1}),$ which does not equal the LHS of the problem statement. So, the statement is false. To make it true, change the LHS to $\displaystyle \log(\frac{x+2}{x-1})$
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