Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 12 - Exponential Functions and Logarithmic Functions - 12.4 Properties of Logarithmic Functions - 12.4 Exercise Set - Page 811: 90



Work Step by Step

Any solution x, if one exists, must be positive for the equation to be defined. LHS: apply $\displaystyle \log_{a}\frac{M}{N}=\log_{a}M-\log_{a}N$ $\log_{10}10^{3}=3$, so we substitute this for the RHS. $\log_{10} \displaystyle \frac{2000}{x} = \log_{10}1000$ ... logarithmic functions are one-to-one, so $\displaystyle \frac{2000}{x}=1000\qquad$ ... multiply with $\displaystyle \frac{x}{1000}$ $2=x$
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