Solve 2/6logz^22/6-4/6log24/6

$$\frac { 2 } { 6 } \log z ^ { 2 } \frac { 2 } { 6 } - \frac { 4 } { 6 } \log 2 \frac { 4 } { 6 }$$

Factor

$$\frac{\log_{10}\left(e\right)\left(\ln(z^{2})+\ln(\frac{3}{64})\right)}{3}$$

Solution Steps

Factor out \frac{1}{3}.

$$\frac{\log_{10}\left(\frac{z^{2}}{3}\right)-2\log_{10}\left(\frac{8}{3}\right)}{3}$$

Consider \ln(\frac{1}{3}z^{2})\times \frac{1}{\ln(10)}-2\ln(\frac{1}{6}\left(12+4\right))\times \frac{1}{\ln(10)}. Factor out \frac{1}{\ln(10)}.

$$\frac{\ln(\frac{z^{2}}{3})-2\ln(\frac{8}{3})}{\ln(10)}$$

Rewrite the complete factored expression.

$$\frac{\ln(\frac{z^{2}}{3})-2\ln(\frac{8}{3})}{3\ln(10)}$$

Evaluate

$$\frac{\log(e)\left(\ln(z^{2})+\ln(\frac{3}{64})\right)}{3}$$