Answer
$y=\dfrac{Cx^2}{x+1}$
Work Step by Step
We know that:
(1) $\log_a {x^n}=n\cdot \log_a {x}$;
(2) $\log_a {x}+\log_a {y}=\log_a {(x\cdot y)}$; and
(3) $\log_a {x}-\log_a {y}=\log_a {(\frac{x}{y})}$
Use the rules above to obtain:
$\ln{y}=\ln{(x^2)}-\ln{(x+1)}+\ln{(C)}\\
\ln{y}=\ln{\left(\frac{x^2}{x+1}\right)}+\ln{C}\\
\ln{y}=\ln{\left(\frac{x^2(C)}{x+1}\right)}\\
\ln{y}=\ln{\left(\frac{Cx^2}{x+1}\right)}
$
Use the rule $\log_a{M}=\log_a{N} \longrightarrow M=N$ to obtain
$y=\frac{Cx^2}{x+1}$
