Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 9 - Review: 122

Answer

$x=\dfrac{7}{2}$

Work Step by Step

Express both sides of the equation with the same base. Once the bases are the same, then equate the exponents. That is, \begin{array}{l} 9^{x-2}=27\\\\ (3^2)^{x-2}=3^3\\\\ 3^{2x-4}=3^3\\\\ 2x-4=3\\\\ 2x=7\\\\ x=\dfrac{7}{2} .\end{array}
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