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: 29

Answer

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

Work Step by Step

First, we let $\log_{7}{\sqrt7} = x$ RECALL: $\log_b{y} =x \longrightarrow b^x=y$ Use the rule above, where $y=\sqrt7$ and $b=7$, to obtain: $7^x=\sqrt7$ Write $\sqrt7$ as $ 7^{\frac{1}{2}}$ to obtain: $7^x=7^{\frac{1}{2}}$ Use the rule "If $a^x=a^y$, then $x=y$" to obtain: $x=\frac{1}{2}$
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