College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 6 - Section 6.6 - Logarithmic and Exponential Equations - 6.6 Assess Your Understanding: 12

Answer

$x=\frac{1}{3}$

Work Step by Step

RECALL: (1) $\log_a{b} = \log_a{c} \longrightarrow b=c$ (2) $n\cdot \log_a{b} = \log_a{(b^n)}$ (3) $\log_a{a} = 1$ Use rule (2) above to obtain: $\log_4{(x^{-2})}=\log_4{9}$ Use rule (1) above to obtain: $x^{-2}=9$ Use the rule $x^{-m} = \frac{1}{x^m}$ to obtain: $\frac{1}{x^2}=9$ Cross-multiply to obtain: $9(x^2)=1(1) \\9x^2=1 \\x^2=\frac{1}{9} \\x^2=(\frac{1}{3})^2$ Use the rule $a^m=b^m \longrightarrow a=b$ to obtain: $x=\frac{1}{3}$
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