College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 4, Exponential and Logarithmic Functions - Section 4.3 - Logarithmic Functions - 4.3 Exercises: 38

Answer

(a) $x=\dfrac{1}{e}$ (b) $x=-1$

Work Step by Step

RECALL: (1) $\ln{x}=y \longrightarrow e^y=x$ (2) $a^{-m}=\dfrac{1}{a^m}, a\ne0$ (a) Use rule (1) above to obtain: $\begin{array}{ccc} &e^{-1}&=&x \end{array}$ Use rule (2) above to obtain: $\dfrac{1}{e}=x$ (b) Use rule (1) above to obtain: $\begin{array}{ccc} &e^x&=&\dfrac{1}{e} \end{array}$ Use the rule (2) above to obtain: $e^x=e^{-1}$ Use the rule $a^m=a^n \longrightarrow m=n$ to obtain: $x=-1$
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