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: 13

Answer

$\log_8{2}=\frac{1}{3}$

Work Step by Step

RECALL: (i) $\sqrt[n]{a}=a^{\frac{1}{n}}.$ (ii) $b^y=x \longleftrightarrow \log_b{x} =y .$ Use rule (i) above to obtain $8^{\frac{1}{3}}=2.$ Use rule (ii) above to obtain $8^{\frac{1}{3}} = 2 \longrightarrow \log_8{2}=\frac{1}{3}.$ Thus, the equivalent logarithmic form of the given expression is $\log_8{2}=\frac{1}{3}.$
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