Solve 3/4log_{2}(5x)-3log_{2}(2y)+7log_{2}(z)

$$\frac { 3 } { 4 } \log _ { 2 } ( 5 x ) - 3 \log _ { 2 } ( 2 y ) + 7 \log _ { 2 } ( z )$$

Factor

$$\frac{\frac{3\ln(x)+28\ln(z)-12\ln(y)+3\ln(5)}{\ln(2)}-12}{4}$$

Solution Steps

Factor out \frac{1}{4}.

$$\frac{3\log_{2}\left(5x\right)-12\log_{2}\left(2y\right)+28\log_{2}\left(z\right)}{4}$$

Consider 3\ln(5x)\times \frac{1}{\ln(2)}-12\ln(2y)\times \frac{1}{\ln(2)}+28\ln(z)\times \frac{1}{\ln(2)}. Factor out \frac{1}{\ln(2)}.

$$\frac{3\ln(5x)-12\ln(2y)+28\ln(z)}{\ln(2)}$$

Rewrite the complete factored expression.

$$\frac{3\ln(5x)-12\ln(2y)+28\ln(z)}{4\ln(2)}$$

Evaluate

$$\frac{3\ln(x)+28\ln(z)-12\ln(y)+\ln(\frac{125}{4096})}{4\ln(2)}$$