Question

expand \\(\ln \frac{6x^2}{y^4}\\).\\(\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

$\ln(6x^2) - \ln(y^4) = \ln6 + \ln(x^2) - \ln(y^4)$

Step3: Apply log power rule

$\ln6 + \ln(x^2) - \ln(y^4) = \ln6 + 2\ln x - 4\ln y$

Answer:

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