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: 16

Answer

$9$

Work Step by Step

Note that $\sqrt{7} = 7^{\frac{1}{2}}$. Write $\sqrt{7}$ as $7^{\frac{1}{2}}$ to obtain: $7^{\frac{x-2}{6}}=7^{\frac{1}{2}}$ Use the rule $a^m=a^n \longrightarrow m=n$ to obtain: $\dfrac{x-2}{6} = \dfrac{1}{2}$ Cross-multiply to obtain: $2(x-2) = 6(1) \\2x-12=6$ Add 12 on both sides of the equation to obtain: $2x=18$ Divide 2 on both sides of the equation to obtain: $x = 9$
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