Expand the Logarithmic Expression log base 4 of ( square root of f)/64

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

Rewrite $\log_{4} (\frac{\sqrt{f}}{64})$ as $\log_{4} (\sqrt{f}) - \log_{4} (64)$ .

$\log_{4} (\sqrt{f}) - \log_{4} (64)$

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{f}$ as $f^{\frac{1}{2}}$ .

$\log_{4} (f^{\frac{1}{2}}) - \log_{4} (64)$

Expand $\log_{4} (f^{\frac{1}{2}})$ by moving $\frac{1}{2}$ outside the logarithm.

$\frac{1}{2} \log_{4} (f) - \log_{4} (64)$

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

$\frac{1}{2} \log_{4} (f) - 1 \cdot 3$

Multiply $- 1$ by $3$ .

$\frac{1}{2} \log_{4} (f) - 3$

Combine $\frac{1}{2}$ and $\log_{4} (f)$ .

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