College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter 4 - Section 4.3 - Logarithmic Functions - Summary Exercises on Inverse, Exponential, and Logarithmic Functions: 28

Answer

$x=-3$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given equation, $ x=\log_{10} 0.001 ,$ use the properties of logarithms to find an equivalent expression for the logarithmic expression. $\bf{\text{Solution Details:}}$ Using exponents, the value $0.001$ is equivalent to $10^{-3}.$ Hence, the equation above is equivalent to \begin{array}{l}\require{cancel} x=\log_{10} 10^{-3} .\end{array} Using the Power Rule of Logarithms, which is given by $\log_b x^y=y\log_bx,$ the equation above is equivalent to \begin{array}{l}\require{cancel} x=-3\log_{10} 10 .\end{array} Since $\log_b b=1,$ the equation above is equivalent to \begin{array}{l}\require{cancel} x=-3(1) \\\\ x=-3 .\end{array}
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