Solve (2log5x^5log6)-2log24

$$( 2 \log 5 x ^ { 5 } \log 6 ) - 2 \log 24$$

Factor

$$\frac{2\left(\ln(2)\left(5\ln(x)+\ln(\frac{1}{600})\right)+5\ln(3)\ln(x)\right)}{\ln(10)^{2}}$$

Solution Steps

Factor out 2.

$$2\left(\log_{10}\left(5x^{5}\right)\log_{10}\left(6\right)-\log_{10}\left(24\right)\right)$$

Consider \ln(5x^{5})\ln(6)\ln(10)^{-2}-\ln(24)\times \frac{1}{\ln(10)}. Factor out \frac{1}{\ln(10)}.

$$\frac{\ln(6)\log_{10}\left(5x^{5}\right)-\ln(24)}{\ln(10)}$$

Rewrite the complete factored expression.

$$\frac{2\left(\ln(6)\log_{10}\left(5x^{5}\right)-\ln(24)\right)}{\ln(10)}$$

Evaluate

$$\frac{2\left(5\ln(2)\ln(x)+5\ln(3)\ln(x)+\ln(\frac{1}{600})\ln(2)\right)}{\ln(10)^{2}}$$