Solve -2/6log^2z/6-4/6log2*4/6

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

Factor

$$\frac{\log_{10}\left(e\right)\left(-\ln(z^{2})+\ln(\frac{81}{4})\right)}{3}$$

Solution Steps

Factor out \frac{1}{3}.

$$\frac{-\log_{10}\left(\left(\frac{z}{6}\right)^{2}\right)-2\log_{10}\left(\frac{4}{3}\right)}{3}$$

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

$$\frac{-\ln(\left(\frac{z}{6}\right)^{2})-2\ln(\frac{4}{3})}{\ln(10)}$$

Rewrite the complete factored expression.

$$\frac{-\ln(\left(\frac{z}{6}\right)^{2})-2\ln(\frac{4}{3})}{3\ln(10)}$$

Evaluate

$$\frac{\log(e)\left(-\ln(z^{2})+\ln(\frac{81}{4})\right)}{3}$$