Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 4 - Section 4.5 - Exponential and Logarithmic Functions - 4.5 Exercises - Page 368: 72

Answer

$x \approx -1.97$ and $x \approx 1.06$

Work Step by Step

To solve the given equation by graphing using a graphing device, let each side of the equation represent a function to obtain: $y=x$ and $y=\ln{(4-x^2)}$ To find the solution/s, perform the following steps: (1) Graph both functions on the same coordinate plane. (refer to the image below for the graph) (2) Identify the point/s that are common to both graphs. The x-coordinate of these points are the solutions to the given equation since they satisfy both functions. Note that the graphs share the common points: $(-1.965, -1.965)$ $(1.058, 1.058)$ Therefore, the solution to the given equation rounded-off to two decimal places are: $x \approx -1.97$ and $x \approx 1.06$
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