Solve 2-log_{2}2^6-log_{2}2^-3

$$2 - \log _ { 2 } 2 ^ { 6 } - \log _ { 2 } 2 ^ { - 3 }$$

Evaluate

$$-1$$

Solution Steps

Calculate 2 to the power of 6 and get 64.

$$2-\log_{2}\left(64\right)-\log_{2}\left(2^{-3}\right)$$

The base 2 logarithm of 64 is 6.

$$2-6-\log_{2}\left(2^{-3}\right)$$

Subtract 6 from 2 to get -4.

$$-4-\log_{2}\left(2^{-3}\right)$$

Calculate 2 to the power of -3 and get \frac{1}{8}.

$$-4-\log_{2}\left(\frac{1}{8}\right)$$

The base 2 logarithm of \frac{1}{8} is -3.

$$-4-\left(-3\right)$$

The opposite of -3 is 3.

$$-4+3$$

Add -4 and 3 to get -1.

$$-1$$

Factor

$$-1$$