Solve (log_{2}4+log_{3}27)(log_{2}16+2^log_{23})

$$( \log _ { 2 } 4 + \log _ { 3 } 27 ) ( \log _ { 2 } 16 + 2 ^ { \log _ { 2 } 3 } )$$

Evaluate

$$35$$

Solution Steps

The base 2 logarithm of 4 is 2.

$$\left(2+\log_{3}\left(27\right)\right)\left(\log_{2}\left(16\right)+2^{\log_{2}\left(3\right)}\right)$$

The base 3 logarithm of 27 is 3.

$$\left(2+3\right)\left(\log_{2}\left(16\right)+2^{\log_{2}\left(3\right)}\right)$$

Add 2 and 3 to get 5.

$$5\left(\log_{2}\left(16\right)+2^{\log_{2}\left(3\right)}\right)$$

The base 2 logarithm of 16 is 4.

$$5\left(4+2^{\log_{2}\left(3\right)}\right)$$

Apply rule a^{\log_{a}\left(b\right)}=b, where a=2 and b=3.

$$5\left(4+3\right)$$

Add 4 and 3 to get 7.

$$5\times 7$$

Multiply 5 and 7 to get 35.

$$35$$

Factor

$$5\times 7$$