Solve x/4ln2+lnfrac{sqrt{2}}{2}

$$\frac { x } { 4 } \ln 2 + \ln \frac { \sqrt { 2 } } { 2 }$$

Factor

$$\frac{\ln(2)\left(x-2\right)}{4}$$

Solution Steps

Factor out \frac{1}{4}.

$$\frac{x\log_{e}\left(2\right)+4\log_{e}\left(\frac{\sqrt{2}}{2}\right)}{4}$$

Consider x\ln(2)\times \frac{1}{\ln(e)}+4\ln(\frac{1}{2}\sqrt{2})\times \frac{1}{\ln(e)}. Factor out \frac{1}{\ln(e)}.

$$\frac{x\ln(2)+4\ln(\frac{\sqrt{2}}{2})}{\ln(e)}$$

Rewrite the complete factored expression.

$$\frac{x\ln(2)+4\ln(\frac{\sqrt{2}}{2})}{4\ln(e)}$$

Evaluate

$$\frac{\ln(2)\left(x-2\right)}{4}$$