Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 1 - Functions - Review Exercises - Page 52: 23

Answer

$$x = 2$$

Work Step by Step

$$\eqalign{ & {\log _{10}}{x^2} + 3{\log _{10}}x = {\log _{10}}32 \cr & {\text{Write 32 as }}{{\text{2}}^5} \cr & {\log _{10}}{x^2} + 3{\log _{10}}x = {\log _{10}}{2^5} \cr & {\text{Apply the power property }}a\log b = \log {b^a} \cr & {\log _{10}}{x^2} + {\log _{10}}{x^3} = {\log _{10}}{2^5} \cr & {\text{Apply the product property }}\log a + \log b = \log ab \cr & {\log _{10}}\left( {{x^2} \cdot {x^3}} \right) = {\log _{10}}{2^5} \cr & {\log _{10}}\left( {{x^5}} \right) = {\log _{10}}{2^5} \cr & {\text{Then }} \cr & {\text{1}}{{\text{0}}^{{{\log }_{10}}\left( {{x^5}} \right)}} = {\text{1}}{{\text{0}}^{{{\log }_{10}}\left( {{2^5}} \right)}} \cr & {x^5} = {2^5} \cr & {\text{Simplifying}} \cr & x = 2 \cr} $$
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