Solve 1/3log(x)-3log(y-1)+log(z)

$$\frac { 1 } { 3 } \log ( x ) - 3 \log ( y - 1 ) + \log ( z )$$

Factor

$$\frac{\log_{10}\left(e\right)\left(-9\ln(y-1)+\ln(x)+3\ln(z)\right)}{3}$$

Solution Steps

Factor out \frac{1}{3}.

$$\frac{\log_{10}\left(x\right)-9\log_{10}\left(y-1\right)+3\log_{10}\left(z\right)}{3}$$

Consider \ln(x)\times \frac{1}{\ln(10)}-9\ln(y-1)\times \frac{1}{\ln(10)}+3\ln(z)\times \frac{1}{\ln(10)}. Factor out \frac{1}{\ln(10)}.

$$\frac{\ln(x)-9\ln(y-1)+3\ln(z)}{\ln(10)}$$

Rewrite the complete factored expression.

$$\frac{\ln(x)-9\ln(y-1)+3\ln(z)}{3\ln(10)}$$

Evaluate

$$\frac{\log(e)\left(-9\ln(y-1)+\ln(x)+3\ln(z)\right)}{3}$$