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: 44

Answer

a.) $x = 36$ b.) $x = 27$

Work Step by Step

$Use$ $the$ $definition$ $of$ $the$ $logarithmic$ $function$ $to$ $find$ $x:$ a.) $\log_x 6 = \frac{1}{2}$ b.) $\log_x 3 = \frac{1}{3}$ a.) $\log_x 6 = \frac{1}{2}$ Rewrite the logarithmic form to exponential form: $\log_b a = c \rightarrow b^c = a$ $$\log_x 6 = \frac{1}{2} \rightarrow x^{\frac{1}{2}} = 6$$ Rewrite 6 as $36^{\frac{1}{2}}$ [Note: $36^{\frac{1}{2}} = \sqrt 36 = 6$] $$x^{\frac{1}{2}} = 36^{\frac{1}{2}}$$ $$x = 36$$ b.) $\log_x 3 = \frac{1}{3}$ Rewrite the logarithmic form to exponential form: $\log_b a = c \rightarrow b^c = a$ $$\log_x 3 = \frac{1}{3} \rightarrow x^{\frac{1}{3}} = 3$$ Rewrite 3 as $27^{\frac{1}{3}}$ [Note: $27^{\frac{1}{3}} = \sqrt[3] 27 = 3$] $$x^{\frac{1}{3}} = 27^{\frac{1}{3}}$$ $$x = 27$$
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