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: 22

Answer

$x=\dfrac{3-\ln16}{5}\approx0.045482$

Work Step by Step

$e^{3-5x}=16$ Apply $\ln$ to both sides of the equation: $\ln e^{3-5x}=\ln16$ The exponent $3-5x$ can be taken down to multiply in front of its respective $\ln$: $(3-5x)\ln e=\ln16$ Since $\ln e=1$, the equation becomes: $3-5x=\ln16$ Solve for $x$: $-5x=\ln16-3$ $x=-\dfrac{\ln16-3}{5}=\dfrac{3-\ln16}{5}\approx0.045482$
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.