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: 31

Answer

$x=-2$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given equation, $ \log_{10} 0.01=x ,$ use the properties of logarithms to find an equivalent expression for the logarithmic expression. $\bf{\text{Solution Details:}}$ Using exponents, the value $0.01$ is equivalent to $10^{-2}.$ Hence, the equation above is equivalent to \begin{array}{l}\require{cancel} \log_{10} 10^{-2}=x .\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} -2\log_{10} 10=x .\end{array} Since $\log_b b=1,$ the equation above is equivalent to \begin{array}{l}\require{cancel} -2(1)=x \\\\ -2=x \\\\ x=-2 .\end{array}
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