Solve 3/8xlog_{2}8/3+1/4xlog_{2}4+1/4log_{2}4+frac{1}{8}log_{2}8

$$\frac { 3 } { 8 } x \log _ { 2 } \frac { 8 } { 3 } + \frac { 1 } { 4 } x \log _ { 2 } 4 + \frac { 1 } { 4 } \log _ { 2 } 4 + \frac { 1 } { 8 } \log _ { 2 } 8$$

Factor

$$\frac{-3\log_{2}\left(3\right)x+13x+7}{8}$$

Solution Steps

Factor out \frac{1}{8}.

$$\frac{3x\log_{2}\left(\frac{8}{3}\right)+2x\log_{2}\left(4\right)+2\log_{2}\left(4\right)+\log_{2}\left(8\right)}{8}$$

Consider 3x\ln(\frac{8}{3})\times \frac{1}{\ln(2)}+2x\ln(4)\times \frac{1}{\ln(2)}+2\ln(4)\times \frac{1}{\ln(2)}+\ln(8)\times \frac{1}{\ln(2)}. Factor out \frac{1}{\ln(2)}.

$$\frac{3x\ln(\frac{8}{3})+4x\ln(2)+7\ln(2)}{\ln(2)}$$

Rewrite the complete factored expression.

$$\frac{3x\ln(\frac{8}{3})+4x\ln(2)+7\ln(2)}{8\ln(2)}$$

Evaluate

$$\frac{-3\log_{2}\left(3\right)x+13x+7}{8}$$