Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 9 - Section 9.5 - Exponential and Logarithmic Equations - Exercise Set: 92

Answer

$x=1$

Work Step by Step

RECALL: (1) $a^m \cdot a^n = a^{m+n}$ (2) If $a^m=a^n$, then $m=n$ Use rule (1) above to obtain: $3^{x+2+x}=81 \\3^{2x+2}=81$ Note that $81=3^4$. Write $81$ as $3^4$ to obtain: $3^{2x+2} = 3^4$ Use rule (2) above to obtain: $2x+2=4$ Subtract $2$ on both sides of the equation to obtain: $2x = 2$ Divide $2$ on both sides of the equation to obtain: $x=1$
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