College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter 4 - Section 4.2 - Exponential Functions - 4.2 Exercises: 71

Answer

$x=-7$

Work Step by Step

We rewrite the 4 on the left, so that the base is $2$ on both sides. $4^{x-2}=2^{3x+3}$ $(2^2)^{x-2}=2^{3x+3}$ By the law of exponents: $(a^x)^y=a^{xy}$ $(2^2)^{x-2}=2^{2x-4}$ Then we set the exponents equal, because the two sides with the same base are equal only if the powers are equal too: if $b^m=b^n$ and $b \ne0$ , $b \ne1$ then $m=n$ $2x-4=3x+3$ $-7=x$
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