Evaluate ( log of 100-2 log base 4 of 64)/( log base 7 of 7)

$\frac{\log (100) - 2 \log_{4} (64)}{\log_{7} (7)}$

Step 1

Simplify the numerator.

Logarithm base $10$ of $100$ is $2$ .

$\frac{2 - 2 \log_{4} (64)}{\log_{7} (7)}$

Logarithm base $4$ of $64$ is $3$ .

$\frac{2 - 2 \cdot 3}{\log_{7} (7)}$

Multiply $- 2$ by $3$ .

$\frac{2 - 6}{\log_{7} (7)}$

Subtract $6$ from $2$ .

$\frac{- 4}{\log_{7} (7)}$

Step 2

Logarithm base $7$ of $7$ is $1$ .

$\frac{- 4}{1}$

Step 3

Divide $- 4$ by $1$ .

$- 4$