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: 10

Answer

$$ x=-4.$$

Work Step by Step

We have $$ \left(b^{2}\right)^{x+1}=b^{-6} \Longrightarrow b^{2x+2}=b^{-6}. $$ Since the bases are equal, then the exponents are equal and hence we get $$2x+2=-6\Longrightarrow 2x=-8 \Longrightarrow x=-4.$$
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