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: 28


$\frac{5}{2}$$\log t$

Work Step by Step

$Expand$ $the$ $expression$: $\log \sqrt{t^5}$ Rewrite the square root $\log (t^5)^{\frac{1}{2}}$ Multiply the exponents together $\log t^{\frac{5}{2}}$ [$\frac{5}{1}$ $\times$ $\frac{1}{2}$ = $\frac{5}{2}$] Apply the Third Law of Logarithms $\log t^{\frac{5}{2}}$ = $\frac{5}{2}$$\log t$
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