Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 12 - Section 12.3 - Exponential Functions - Exercise Set: 31

Answer

$x=-\dfrac{1}{3}$

Work Step by Step

$27^{x+1}=9$ Rewrite $27$ as $3^{3}$ and $9$ as $3^{2}$: $(3^{3})^{x+1}=3^{2}$ Transform the left side of the equation into a power that has the product of $3$ and $x+1$ as its exponent: $3^{3x+3}=3^{2}$ If $3^{3x+3}=3^{2}$, then $3x+3=2$ $3x+3=2$ Solve for $x$: $3x=2-3$ $3x=-1$ $x=-\dfrac{1}{3}$
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