Solve logx+1/2logy-3logz

$$\log x + \frac { 1 } { 2 } \log y - 3 \log z$$

Factor

$$\frac{\log_{10}\left(e\right)\left(\ln(y)+2\ln(x)-6\ln(z)\right)}{2}$$

Solution Steps

Factor out \frac{1}{2}.

$$\frac{2\log_{10}\left(x\right)+\log_{10}\left(y\right)-6\log_{10}\left(z\right)}{2}$$

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

$$\frac{2\ln(x)+\ln(y)-6\ln(z)}{\ln(10)}$$

Rewrite the complete factored expression.

$$\frac{2\ln(x)+\ln(y)-6\ln(z)}{2\ln(10)}$$

Evaluate

$$\frac{\log(e)\left(\ln(y)+2\ln(x)-6\ln(z)\right)}{2}$$