Solve log_{2}8^3-2log_{3}27+log_{5}125

$$\log _ { 2 } 8 ^ { 3 } - 2 \log _ { 3 } 27 + \log _ { 5 } 125$$

Evaluate

$$6$$

Solution Steps

Calculate 8 to the power of 3 and get 512.

$$\log_{2}\left(512\right)-2\log_{3}\left(27\right)+\log_{5}\left(125\right)$$

The base 2 logarithm of 512 is 9.

$$9-2\log_{3}\left(27\right)+\log_{5}\left(125\right)$$

The base 3 logarithm of 27 is 3.

$$9-2\times 3+\log_{5}\left(125\right)$$

Multiply 2 and 3 to get 6.

$$9-6+\log_{5}\left(125\right)$$

Subtract 6 from 9 to get 3.

$$3+\log_{5}\left(125\right)$$

The base 5 logarithm of 125 is 3.

$$3+3$$

Add 3 and 3 to get 6.

$$6$$

Factor

$$2\times 3$$