Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 4 - Exponential and Logarithmic Functions - Section 4.4 Logarithmic Functions - 4.4 Assess Your Understanding - Page 322: 111

Answer

(a) $(-\frac{1}{2},\infty)$. (b) $2$, $(40,2)$. (c) $121$, $(121,3)$. (d) $ 4$.

Work Step by Step

Given $G(x)=log_3(2x+1)-2$, we have: (a) the domain $2x+1\gt0$ or $(-\frac{1}{2},\infty)$. (b) $G(40)=log_3(2(40)+1)-2=2$ giving point $(40,2)$. (c) $G(x)=log_3(2x+1)-2=3 \Longrightarrow 2x+1=3^5 \Longrightarrow x=121$ giving point $(121,3)$. (d) $G(x)=log_3(2x+1)-2=0 \Longrightarrow 2x+1=3^2 \Longrightarrow x=4$.
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