## Precalculus: Mathematics for Calculus, 7th Edition

$\ln 3$ + 2$\ln x$ - 10$\ln (x+1)$
$Expand$ $the$ $expression$: $\ln \frac{3x^2}{(x+1)^{10}}$ 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$\ln (x+1)$