Evaluate ( log base 4 of 64)/( log base 4 of 4)

$\frac{\log_{4} (64)}{\log_{4} (4)}$

Rewrite $\log_{4} (64)$ as $\log_{4} (2^{6})$ .

$\frac{\log_{4} (2^{6})}{\log_{4} (4)}$

Expand $\log_{4} (2^{6})$ by moving $6$ outside the logarithm.

$\frac{6 \log_{4} (2)}{\log_{4} (4)}$

Rewrite $\log_{4} (4)$ as $\log_{4} (2^{2})$ .

$\frac{6 \log_{4} (2)}{\log_{4} (2^{2})}$

Expand $\log_{4} (2^{2})$ by moving $2$ outside the logarithm.

$\frac{6 \log_{4} (2)}{2 \log_{4} (2)}$

Cancel the common factor of $6$ and $2$ .

Factor $2$ out of $6 \log_{4} (2)$ .

$\frac{2 (3 \log_{4} (2))}{2 \log_{4} (2)}$

Cancel the common factors.

Factor $2$ out of $2 \log_{4} (2)$ .

$\frac{2 (3 \log_{4} (2))}{2 (\log_{4} (2))}$

Cancel the common factor.

$\frac{2 (3 \log_{4} (2))}{2 \log_{4} (2)}$

Rewrite the expression.

$\frac{3 \log_{4} (2)}{\log_{4} (2)}$

Cancel the common factor of $\log_{4} (2)$ .

Cancel the common factor.

$\frac{3 \log_{4} (2)}{\log_{4} (2)}$

Divide $3$ by $1$ .

$3$