Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 4 - Section 4.4 - Laws of Logarithms - 4.4 exercises - Page 359: 44


$\ln 3$ + 2$\ln x$ - 10$\ln (x+1)$

Work Step by Step

$Expand$ $the$ $expression$: $\ln \frac{3x^2}{(x+1)^{10}}$ Apply the Second Law of Logarithms $\ln \frac{3x^2}{(x+1)^{10}}$ = $\ln 3x^2$ - $\ln (x+1)^{10}$ Apply the First Law of Logarithms for $\ln 3x^2$ $\ln (3\times x^2)$ = $\ln 3$ + $\ln x^2$ $\ln 3$ + $\ln x^2$ - $\ln (x+1)^{10}$ Apply the Third Law of Logarithms for $\ln x^2$ and $\ln (x+1)^{10}$ $\ln x^2$ = 2$\ln x$ $\ln (x+1)^{10}$ = 10$\ln (x+1)$ Assemble the expression $\ln 3$ + 2$\ln x$ - 10$\ln (x+1)$
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