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: 7


$$ x=-\frac{1}{3}.$$

Work Step by Step

We have $$ 4^{-x}=2^{x+1} \Longrightarrow (2^2)^{-2x}=2^{x+1} \Longrightarrow 2^{-2x}=2^{x+1}. $$ Since the bases are equal, then the exponents are equal and hence we get $$-2x=x+1\Longrightarrow -3x=1\Longrightarrow x=-\frac{1}{3}.$$
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