Solve log(a)+1/2log(b)-2log(c)

$$\log ( a ) + \frac { 1 } { 2 } \log ( b ) - 2 \log ( c )$$

Factor

$$\frac{\log_{10}\left(e\right)\left(\ln(b)+2\ln(a)-4\ln(c)\right)}{2}$$

Solution Steps

Factor out \frac{1}{2}.

$$\frac{2\log_{10}\left(a\right)+\log_{10}\left(b\right)-4\log_{10}\left(c\right)}{2}$$

Consider 2\ln(a)\times \frac{1}{\ln(10)}+\ln(b)\times \frac{1}{\ln(10)}-4\ln(c)\times \frac{1}{\ln(10)}. Factor out \frac{1}{\ln(10)}.

$$\frac{2\ln(a)+\ln(b)-4\ln(c)}{\ln(10)}$$

Rewrite the complete factored expression.

$$\frac{2\ln(a)+\ln(b)-4\ln(c)}{2\ln(10)}$$

Evaluate

$$\frac{\log(e)\left(\ln(b)+2\ln(a)-4\ln(c)\right)}{2}$$