Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 6 - Inverse Functions - 6.4* General Logarithmic and Exponential Functions - 6.4* Exercise: 19


(a) 265 mi (b) 1084588 miles

Work Step by Step

As we know 1 ft = 12 inches This implies 2 ft = 24 inches $f(24)=(24)^{2} =576$ inches This implies $f(24)=\frac{576}{12}$ ft $=48$ ft As per statement, $g(x)=2^{x}=g(24)=2^{24}$inches Hence, $g(24)=2^{24}$inches Since, $1$ mile $=5280$ ft Thus, $g(24)=\frac{2^{24}}{12\times 5280}=265$ mi (b) Since 3 ft = 36 inches Thus, $log_{2}x=36$ Using formula $log_{b}x=y=b^{y}=x$ This implies $x=2^{36}$ inches Hence, $x= \frac{2^{36}}{12\times 5280}\approx1084588$ miles
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.