Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 7 - Exponential Functions - 7.1 Derivative of f(x)=bx and the Number e - Exercises - Page 327: 5


$$ x=-\frac{1}{2}.$$

Work Step by Step

We have $$3^x=\left(\frac{1}{3}\right)^{x+1}\Longrightarrow 3^x=3^{-x-1}.$$ Since the bases are equal, then the exponents are equal and we get $$ x=-x-1\Longrightarrow 2x=-1 \Longrightarrow x=-\frac{1}{2}.$$
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