Precalculus: Mathematics for Calculus, 7th Edition

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

Chapter 4 - Review - Exercises: 40



Work Step by Step

$Evaluate$ $the$ $expression$ $without$ $using$ $a$ $calculator:$ $\log_3 \sqrt {243}$ Rewrite the root to exponent form $$\log_3 (243)^{\frac{1}{2}}$$ Rewrite 243 as $3^5$ [Note: $3^5 = 3\times3\times3\times3\times3 = 243$] $$\log_3 (3^5)^{\frac{1}{2}} \rightarrow \log_3 3^{\frac{5}{1}\times\frac{1}{2}}$$ $$\log_3 3^{\frac{5}{2}}$$ Use the Third Property of Logarithms: $\log_a a^x = x$ $$\log_3 3^{\frac{5}{2}} = \frac{5}{2}$$
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