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 9.3 - Logarithmic Functions - Exercise Set: 34

Answer

$x = \frac{1}{2}$

Work Step by Step

Let $\log_{81}{9} = x$ RECALL: $\log_b{y} =x \longrightarrow b^x=y$ Use the rule above, where $y=9$ and $b=81$, to obtain: $81^x=9^{1}$ Write 81 as $9^2$ to obtain: $(9^2)^x=9^{1} \\9^{2x} = 9^{1}$ Use the rule "If $a^x=a^y$, then $x=y$" to obtain: $2x=1 \\x = \frac{1}{2}$
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