College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 4 - Exponential and Logarithmic Functions - Exercise Set 4.2 - Page 466: 46


Please see image .

Work Step by Step

The function $g(x)=\log_{b}x$ (the logarithmic function with base $b$) is the inverse function of the exponential function with base $b,\ f(x)=b^{x}$ The graphs of inverse functions are reflections of the original function, about the line y=x. The base b here is $\displaystyle \frac{1}{4}=0.25.$ Our plan: 1. graph f(x) by plotting several points, (x,f(x)) joining them with a smooth curve, 2. swap the coordinates of the points we got in step 1 to obtain new points (f(x),x). 3. The points in (2.) are reflections of the points in (1.) about the line y=x. We may graph the line y=x to illustrate this. Joining this new set of points, we have graphed g(x)
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