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: 36

Answer

a.) $\frac{1}{9}$ b.) 3

Work Step by Step

$Use$ $the$ $definition$ $of$ $the$ $logarithmic$ $function$ $to$ $find$ $x:$ a.) $\log_3 x = -2$ b.) $\log_5 125 = x$ a.) $\log_3 x = -2$ Rewrite the logarithmic form to exponential form: $\log_b a = c \rightarrow b^c = a$ $\log_3 x = -2 \rightarrow 3^{-2} = x$ $x = 3^{-2} \rightarrow x = \frac{1}{3\times3}$ $x= \frac{1}{9}$ b.) $\log_5 125 = x$ Rewrite the logarithmic form to exponential form: $\log_b a = c \rightarrow b^c = a$ $\log_5 125 =x \rightarrow 5^x = 125$ Rewrite 125 as $5^3$ [Note: $5^3 = 5\times5\times5 = 125$] $5^x = 5^3$ $x = 3$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.