Final Answer
$\ln\left(\frac{\left(x+1\right)^2}{x}\right)$
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Step-by-step Solution
Problem to solve:
$2\ln\left(x+1\right)-\ln\left(x\right)$
Specify the solving method
1
Using the power rule of logarithms: $n\log_b(a)=\log_b(a^n)$, where $n$ equals $2$
$\ln\left(\left(x+1\right)^2\right)-\ln\left(x\right)$
2
The difference of two logarithms of equal base $b$ is equal to the logarithm of the quotient: $\log_b(x)-\log_b(y)=\log_b\left(\frac{x}{y}\right)$
$\ln\left(\frac{\left(x+1\right)^2}{x}\right)$
Final Answer
$\ln\left(\frac{\left(x+1\right)^2}{x}\right)$