Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 12 - Exponential Functions and Logarithmic Functions - 12.3 Logarithmic Functions - 12.3 Exercise Set - Page 804: 113

Answer

If b=0, take, for example $x_{1}=1$ and $x_{2}=2.$ They are obviously different, $x_{1}\neq x_{2}$, but $b^{x_{1}}=0^{1}=0,\qquad b^{x_{2}}=0^{2}=0$, meaning that $b^{x_{1}}=b^{x_{2}}$. If b=1, take, for example $x_{1}=1$ and $x_{2}=2.$ They are obviously different, $x_{1}\neq x_{2}$, but $b^{x_{1}}=1^{1}=1,\qquad b^{x_{2}}=1^{2}=1$, meaning that $b^{x_{1}}=b^{x_{2}}$. The equivalence fails in both cases.

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