Solve log_{2}(2^5*4^7)quad(3)log_{3}27

$$\log _ { 2 } ( 2 ^ { 5 } \times 4 ^ { 7 } ) \quad ( 3 ) \log _ { 3 } 27$$

Evaluate

$$171$$

Solution Steps

Calculate 2 to the power of 5 and get 32.

$$\log_{2}\left(32\times 4^{7}\right)\times 3\log_{3}\left(27\right)$$

Calculate 4 to the power of 7 and get 16384.

$$\log_{2}\left(32\times 16384\right)\times 3\log_{3}\left(27\right)$$

Multiply 32 and 16384 to get 524288.

$$\log_{2}\left(524288\right)\times 3\log_{3}\left(27\right)$$

The base 2 logarithm of 524288 is 19.

$$19\times 3\log_{3}\left(27\right)$$

Multiply 19 and 3 to get 57.

$$57\log_{3}\left(27\right)$$

The base 3 logarithm of 27 is 3.

$$57\times 3$$

Multiply 57 and 3 to get 171.

$$171$$

Factor

$$3^{2}\times 19$$