Solve 1/2log_{a}(x^2y^4)+3log_{a}(xy^2)

$$\frac { 1 } { 2 } \log _ { a } ( x ^ { 2 } y ^ { 4 } ) + 3 \log _ { a } ( x y ^ { 2 } )$$

Factor

$$\frac{\ln(x^{2}y^{4})+6\ln(xy^{2})}{2\ln(a)}$$

Solution Steps

Factor out \frac{1}{2}.

$$\frac{\log_{a}\left(x^{2}y^{4}\right)+6\log_{a}\left(xy^{2}\right)}{2}$$

Consider \ln(x^{2}y^{4})\times \frac{1}{\ln(a)}+6\ln(xy^{2})\times \frac{1}{\ln(a)}. Factor out \frac{1}{\ln(a)}.

$$\frac{\ln(x^{2}y^{4})+6\ln(xy^{2})}{\ln(a)}$$

Rewrite the complete factored expression.

$$\frac{\ln(x^{2}y^{4})+6\ln(xy^{2})}{2\ln(a)}$$

Evaluate

$$\frac{\ln(x^{2}y^{4})+6\ln(xy^{2})}{2\ln(a)}$$