Solve -7/14log_{2}7/14-7/14log_{2}7/14=

$$- \frac { 7 } { 14 } \log _ { 2 } \frac { 7 } { 14 } - \frac { 7 } { 14 } \log _ { 2 } \frac { 7 } { 14 } =$$

Evaluate

$$1$$

Solution Steps

Reduce the fraction \frac{7}{14} to lowest terms by extracting and canceling out 7.

$$-\frac{1}{2}\log_{2}\left(\frac{7}{14}\right)-\frac{7}{14}\log_{2}\left(\frac{7}{14}\right)$$

Reduce the fraction \frac{7}{14} to lowest terms by extracting and canceling out 7.

$$-\frac{1}{2}\log_{2}\left(\frac{1}{2}\right)-\frac{7}{14}\log_{2}\left(\frac{7}{14}\right)$$

The base 2 logarithm of \frac{1}{2} is -1.

$$-\frac{1}{2}\left(-1\right)-\frac{7}{14}\log_{2}\left(\frac{7}{14}\right)$$

Multiply -\frac{1}{2} and -1 to get \frac{1}{2}.

$$\frac{1}{2}-\frac{7}{14}\log_{2}\left(\frac{7}{14}\right)$$

Reduce the fraction \frac{7}{14} to lowest terms by extracting and canceling out 7.

$$\frac{1}{2}-\frac{1}{2}\log_{2}\left(\frac{7}{14}\right)$$

Reduce the fraction \frac{7}{14} to lowest terms by extracting and canceling out 7.

$$\frac{1}{2}-\frac{1}{2}\log_{2}\left(\frac{1}{2}\right)$$

The base 2 logarithm of \frac{1}{2} is -1.

$$\frac{1}{2}-\frac{1}{2}\left(-1\right)$$

Multiply \frac{1}{2} and -1 to get -\frac{1}{2}.

$$\frac{1}{2}-\left(-\frac{1}{2}\right)$$

The opposite of -\frac{1}{2} is \frac{1}{2}.

$$\frac{1}{2}+\frac{1}{2}$$

Add \frac{1}{2} and \frac{1}{2} to get 1.

$$1$$

Factor

$$1$$