Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 4 - Section 4.4 - Laws of Logarithms - 4.4 exercises - Page 359: 16


$- \frac {3}{2}$

Work Step by Step

$\log_5 \frac{1}{\sqrt {125}}$ Rewrite the square root to exponential form $\log_5 \frac{1}{125^{\frac{1}{2}}}$ 125 = $5^{3}$ since 5 $\times$ 5 $\times$ 5 = 125. $\log_5 \frac{1}{(5)^{{3}^{\frac{1}{2}}}}$ When there's a base to a power times a power, we multiply the powers together $\log_5 \frac{1}{5^{\frac{3}{2}}}$ We can move the denominator to the numerator by changing the power to a negative $\log_5 5^{- \frac{3}{2}}$ = $- \frac {3}{2}$
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