expand $ln\frac{6x^{2}}{y^{4}}$.\n$ln\frac{6x^{2}}{y^{4}}=square$

Explanation:

Step1: Apply log - quotient rule

$\ln\frac{6x^{2}}{y^{4}}=\ln(6x^{2})-\ln(y^{4})$

Step2: Apply log - product rule on $\ln(6x^{2})$

$\ln(6x^{2})=\ln6+\ln(x^{2})$

Step3: Apply log - power rule on $\ln(x^{2})$ and $\ln(y^{4})$

$\ln(x^{2}) = 2\ln x$ and $\ln(y^{4})=4\ln y$

Step4: Combine the results

$\ln\frac{6x^{2}}{y^{4}}=\ln6 + 2\ln x-4\ln y$

Answer:

$\ln6 + 2\ln x-4\ln y$