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: 69


$x\approx 2.21$

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: $y=\ln{x}$ (the blue graph) $y=3-x$ (the red graph) (refer to the image below for the graph. The point/s where the graphs intersect are the points where $\ln{x}=3-x$. The x-coordinates of these point are the solutions to the given equation. Note that the graphs intersect at the point $(2.208, 0.792)$. The x-coordinate of this point is $2.208$. Rounded-off to two decimal places, the solution to the given equation is: $x\approx 2.21$
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