Answer
$\ln 3$ + 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$\ln (x+1)$
