Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 3 - Section 3.2 - Exponential Functions - Exercise Set: 82

Answer

$3$

Work Step by Step

RECALL $y=\log{x} \longleftrightarrow 10^y=x.$ Note that $1000=10^3$. Thus, the given expression can be written as $\log{10^3}.$ Let $y=\log{10^3}.$ Use the definition above to obtain $y=\log{10^3} \longrightarrow 10^y=10^3.$ Use the rule "if $a^x=a^y$, then $x=y$" to obtain $y=3.$ Therefore, $\log{1000} = 3.$
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