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 4.5 - Exponential and Logarithmic Functions - 4.5 Exercises - Page 404: 72


$x=\left\{-1.97, 1.06\right\}$

Work Step by Step

To solve the given equation graphically, you have to treat each side of the equation as a function. Thus, using a graphing utility, graph the functions: $y=\ln{x}$ (blue graph) $y=\ln{(4-x^2)}$ (the red graph) (refer to the image below for the graph. The point/s where the graphs intersect are the points where $x=\ln{(4-x^2)}$. The x-coordinates of these point are the solutions to the given equation. Note that the graphs intersect at the points $(-1.965,-1.965)$ and $(1.058, 1.058)$. The x-coordinates of these points are $-1.965$ and $1.058$. Rounded-off to two decimal places, the solutions to the given equation are: $x=\left\{-1.97, 1.06\right\}$.
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