Solve 3log_{2}x-1/3log_{2}(x^2+1)

$$3 \log _ { 2 } x - \frac { 1 } { 3 } \log _ { 2 } ( x ^ { 2 } + 1 )$$

Factor

$$\frac{-\ln(x^{2}+1)+9\ln(x)}{3\ln(2)}$$

Solution Steps

Factor out \frac{1}{3}.

$$\frac{9\log_{2}\left(x\right)-\log_{2}\left(x^{2}+1\right)}{3}$$

Consider 9\ln(x)\times \frac{1}{\ln(2)}-\ln(x^{2}+1)\times \frac{1}{\ln(2)}. Factor out \frac{1}{\ln(2)}.

$$\frac{9\ln(x)-\ln(x^{2}+1)}{\ln(2)}$$

Rewrite the complete factored expression.

$$\frac{9\ln(x)-\ln(x^{2}+1)}{3\ln(2)}$$

Evaluate

$$\frac{-\ln(x^{2}+1)+9\ln(x)}{3\ln(2)}$$