Solve log_{4}64^4-log1000^-3

$$\log _ { 4 } 64 ^ { 4 } - \log 1000 ^ { - 3 }$$

Evaluate

$$21$$

Solution Steps

Calculate 64 to the power of 4 and get 16777216.

$$\log_{4}\left(16777216\right)-\log_{10}\left(1000^{-3}\right)$$

The base 4 logarithm of 16777216 is 12.

$$12-\log_{10}\left(1000^{-3}\right)$$

Calculate 1000 to the power of -3 and get \frac{1}{1000000000}.

$$12-\log_{10}\left(\frac{1}{1000000000}\right)$$

The base 10 logarithm of \frac{1}{1000000000} is -9.

$$12-\left(-9\right)$$

The opposite of -9 is 9.

$$12+9$$

Add 12 and 9 to get 21.

$$21$$

Factor

$$3\times 7$$