Solve 1/2log81-3log2-logz

$$\frac { 1 } { 2 } \log 81 - 3 \log 2 - \log z$$

Factor

$$\log_{10}\left(e\right)\left(-\ln(z)+\ln(\frac{9}{8})\right)$$

Solution Steps

Factor out \frac{1}{2}.

$$\frac{\log_{10}\left(81\right)-6\log_{10}\left(2\right)-2\log_{10}\left(z\right)}{2}$$

Consider \ln(81)\times \frac{1}{\ln(10)}-6\ln(2)\times \frac{1}{\ln(10)}-2\ln(z)\times \frac{1}{\ln(10)}. Factor out \frac{1}{\ln(10)}.

$$\frac{-2\ln(z)+\ln(\frac{81}{64})}{\ln(10)}$$

Rewrite the complete factored expression.

$$\frac{-2\ln(z)+\ln(\frac{81}{64})}{2\ln(10)}$$

Evaluate

$$\frac{\log(e)\left(-2\ln(z)+\ln(\frac{81}{64})\right)}{2}$$