Solve log_{5}w+frac{log_{5}x}{2}+frac{log_{5}y}{2}+frac{log_{5}z}{2}

$$\log _ { 5 } w + \frac { \log _ { 5 } x } { 2 } + \frac { \log _ { 5 } y } { 2 } + \frac { \log _ { 5 } z } { 2 }$$

Factor

$$\frac{\ln(x)+\ln(y)+\ln(z)+2\ln(w)}{2\ln(5)}$$

Solution Steps

Factor out \frac{1}{2}.

$$\frac{2\log_{5}\left(w\right)+\log_{5}\left(x\right)+\log_{5}\left(y\right)+\log_{5}\left(z\right)}{2}$$

Consider 2\ln(w)\times \frac{1}{\ln(5)}+\ln(x)\times \frac{1}{\ln(5)}+\ln(y)\times \frac{1}{\ln(5)}+\ln(z)\times \frac{1}{\ln(5)}. Factor out \frac{1}{\ln(5)}.

$$\frac{2\ln(w)+\ln(x)+\ln(y)+\ln(z)}{\ln(5)}$$

Rewrite the complete factored expression.

$$\frac{2\ln(w)+\ln(x)+\ln(y)+\ln(z)}{2\ln(5)}$$

Evaluate

$$\frac{\ln(x)+\ln(y)+\ln(z)+2\ln(w)}{2\ln(5)}$$