Solve (1/4)logk-2log5+(1/3)log27

$$( 1 / 4 ) \log k - 2 \log 5 + ( 1 / 3 ) \log 27$$

Factor

$$\frac{\log_{10}\left(e\right)\left(\ln(k)+\ln(\frac{81}{390625})\right)}{4}$$

Solution Steps

Factor out \frac{1}{12}.

$$\frac{3\log_{10}\left(k\right)-24\log_{10}\left(5\right)+4\log_{10}\left(27\right)}{12}$$

Consider 3\ln(k)\times \frac{1}{\ln(10)}-24\ln(5)\times \frac{1}{\ln(10)}+4\ln(27)\times \frac{1}{\ln(10)}. Factor out \frac{1}{\ln(10)}.

$$\frac{3\ln(k)+\ln(\frac{531441}{59604644775390625})}{\ln(10)}$$

Rewrite the complete factored expression.

$$\frac{3\ln(k)+\ln(\frac{531441}{59604644775390625})}{12\ln(10)}$$

Evaluate

$$\frac{\log(e)\left(3\ln(k)+\ln(\frac{531441}{59604644775390625})\right)}{12}$$