Precalculus: Mathematics for Calculus, 7th Edition

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

Chapter 4 - Section 4.3 - Logarithmic Functions - 4.3 Exercises: 40

Answer

a.) $x = \frac{1}{2}$ b.)$x = 16$

Work Step by Step

$Use$ $the$ $definition$ $of$ $the$ $logarithmic$ $function$ $to$ $find$ $x:$ a.) $\log_4 2 = x$ b.) $\log_4 x = 2$ a.) $\log_4 2 = x$ Rewrite 2 as $4^{\frac{1}{2}}$ [Note: $4^{\frac{1}{2}} = \sqrt 4 = 2$] $$\log_4 4^{\frac{1}{2}} = x$$ Use the Third Property of Logarithms:$\log_a a^x = x$ $$\log_4 4^{\frac{1}{2}} = x \rightarrow \frac{1}{2} = x$$ $$x = \frac{1}{2}$$ b.) $\log_4 x = 2$ Rewrite the logarithmic form to exponential form: $\log_b a = c \rightarrow b^c = a$ $$\log_4 x = 2 \rightarrow 4^2 = x$$ $$x=16$$
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