Solve 0(10^-5)-log_{10}(1000)*log_{10}(5^2*4)

$$0 ( 10 ^ { - 5 } ) - \log _ { 10 } ( 1000 ) * \log _ { 10 } ( 5 ^ { 2 } * 4 )$$

Evaluate

$$-6$$

Solution Steps

Calculate 10 to the power of -5 and get \frac{1}{100000}.

$$0\times \frac{1}{100000}-\log_{10}\left(1000\right)\log_{10}\left(5^{2}\times 4\right)$$

Multiply 0 and \frac{1}{100000} to get 0.

$$0-\log_{10}\left(1000\right)\log_{10}\left(5^{2}\times 4\right)$$

The base 10 logarithm of 1000 is 3.

$$0-3\log_{10}\left(5^{2}\times 4\right)$$

Calculate 5 to the power of 2 and get 25.

$$0-3\log_{10}\left(25\times 4\right)$$

Multiply 25 and 4 to get 100.

$$0-3\log_{10}\left(100\right)$$

The base 10 logarithm of 100 is 2.

$$0-3\times 2$$

Multiply 3 and 2 to get 6.

$$0-6$$

Subtract 6 from 0 to get -6.

$$-6$$

Factor

$$-6$$