Solve 3/4log_{2}(16x^2)-log_{2}(sqrtx^3)

$$\frac { 3 } { 4 } \log _ { 2 } ( 16 x ^ { 2 } ) - \log _ { 2 } ( \sqrt { x } ^ { 3 } )$$

Factor

$$\frac{3\left(\frac{\ln(x^{2})-2\ln(x)}{\ln(2)}+4\right)}{4}$$

Solution Steps

Factor out \frac{1}{4}.

$$\frac{3\log_{2}\left(16x^{2}\right)-4\log_{2}\left(\left(\sqrt{x}\right)^{3}\right)}{4}$$

Consider 3\ln(16x^{2})\times \frac{1}{\ln(2)}-4\ln(x^{\frac{3}{2}})\times \frac{1}{\ln(2)}. Factor out \frac{1}{\ln(2)}.

$$\frac{3\ln(16x^{2})-4\ln(x^{\frac{3}{2}})}{\ln(2)}$$

Rewrite the complete factored expression.

$$\frac{3\ln(16x^{2})-4\ln(x^{\frac{3}{2}})}{4\ln(2)}$$

Evaluate

$$\frac{3\left(\ln(x^{2})-2\ln(x)+4\ln(2)\right)}{4\ln(2)}$$