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: 43

Answer

a.) $x = 2$ b.) $x = 4$

Work Step by Step

$Use$ $the$ $definition$ $of$ $the$ $logarithmic$ $function$ $to$ $find$ $x:$ a.) $\log_ x 16 = 4$ b.) $\log_ x 8 = \frac{3}{2}$ a.) $\log_ x 16 = 4$ Rewrite the logarithmic form to exponential form: $\log_b a = c \rightarrow b^c = a$ $$\log_x 16 = 4 \rightarrow x^4 = 16$$ Rewrite 16 as $2^4$ [Note: $2^4 = 2\times2\times2\times2 = 16$] $$x^4 = 2^4$$ $$x = 2$$ b.) $\log_ x 8 = \frac{3}{2}$ Rewrite the logarithmic form to exponential form: $\log_b a = c \rightarrow b^c = a$ $$\log_x 8 = \frac{3}{2} \rightarrow x^{\frac{3}{2}} = 8$$ $$x^{\frac{3}{2}\times\frac{2}{3}} = 8^{\frac{2}{3}}$$ $$x = \sqrt[3] {64}$$ $$x = 4$$
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