Solve frac{log_{10}(x^2+1)}{6}-frac{log_{10}(x)}{2}

$$\frac { \log _ { 10 } ( x ^ { 2 } + 1 ) } { 6 } - \frac { \log _ { 10 } ( x ) } { 2 }$$

Factor

$$\frac{\log_{10}\left(e\right)\left(\ln(x^{2}+1)-3\ln(x)\right)}{6}$$

Solution Steps

Factor out \frac{1}{6}.

$$\frac{\log_{10}\left(x^{2}+1\right)-3\log_{10}\left(x\right)}{6}$$

Consider \ln(x^{2}+1)\times \frac{1}{\ln(10)}-3\ln(x)\times \frac{1}{\ln(10)}. Factor out \frac{1}{\ln(10)}.

$$\frac{\ln(x^{2}+1)-3\ln(x)}{\ln(10)}$$

Rewrite the complete factored expression.

$$\frac{\ln(x^{2}+1)-3\ln(x)}{6\ln(10)}$$

Evaluate

$$\frac{\log(e)\left(\ln(x^{2}+1)-3\ln(x)\right)}{6}$$